Proposition isaset_profunctor_quantale_enrichment {C₁ C₂ : univalent_category} (E₁ : enrichment C₁ V) (E₂ : enrichment C₂ V) : isaset (E₁ ↛e E₂). Proof. use isaset_total2. - use isaset_total2. + use funspace_isaset. use funspace_isaset. exact (@isaset_ob_quantale_enrichment_univalent_cat (univalent_category_of_quantale_cosmos V) (self_enrichment V)). + intro F. use isasetdirprod. * use impred_isaset ; intro x₁. use impred_isaset ; intro x₂. use impred_isaset ; intro y. apply homset_property. * use impred_isaset ; intro x. use impred_isaset ; intro y₁. use impred_isaset ; intro y₂. apply homset_property. - intro. apply isasetaprop. apply isaprop_enriched_profunctor_laws. 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.