Proposition isaset_functor_quantale_enrichment {C₁ C₂ : univalent_category} (E₂ : enrichment C₂ V) : isaset (C₁ ⟶ C₂). Proof. use isaset_total2. - use isaset_total2. + use funspace_isaset. use isaset_ob_quantale_enrichment_univalent_cat. exact E₂. + intro F. use impred_isaset ; intro x. use impred_isaset ; intro y. use impred_isaset ; intro f. apply homset_property. - intro. apply isasetaprop. apply isaprop_is_functor. apply homset_property. 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.