Definition disp_univalent_2_0_enriched_cats (HV : is_univalent V) : disp_univalent_2_0 disp_bicat_of_enriched_cats. Proof. use fiberwise_univalent_2_0_to_disp_univalent_2_0. intros C₁ E₁ E₂. use weqhomot. - exact (weq_disp_adjequiv_enriched _ _ ∘ disp_univalent_2_0_enriched_cats_help E₁ E₂ ∘ enrichment_data_hom_path HV _ _ ∘ total2_paths_equiv _ _ _ ∘ path_sigma_hprop _ _ _ (isaprop_enrichment_laws _))%weq. - abstract (intro p ; cbn in p ; induction p ; use subtypePath ; [ intro ; apply isaprop_disp_left_adjoint_equivalence ; [ apply univalent_cat_is_univalent_2_1 | ] ; exact disp_univalent_2_1_enriched_cats | ] ; use subtypePath ; [ intro ; apply isaprop_is_functor_enrichment | ] ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. 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.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.QuantaleEnriched. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Discreteness. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Projection. Section FromEnrichmentPath. End FromEnrichmentPath.