Proposition eq_functor_quantale_enrichment {C₁ C₂ : category} (E₂ : enrichment C₂ V) {F G : C₁ ⟶ C₂} (p : ∏ (x : C₁), F x = G x) : F = G. Proof. use subtypePath. { intro. apply isaprop_is_functor. apply homset_property. } use subtypePath. { intro. repeat (use impred ; intro). apply isaprop_mor_quantale_enrichment_univalent_cat. exact E₂. } use funextsec. exact p. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.PosetCat. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.SelfEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Import MonoidalNotations.