Definition to_enrichment_path : enrichment_data_hom_path_help (pr1 E₁) (pr1 E₂). Proof. simple refine (_ ,, _ ,, _ ,, _ ,, _). - refine (λ x y, _). use make_z_iso. + exact (pr1 F₁ x y). + exact (pr1 F₂ x y). + split. * exact (to_enrichment_path_inv_left x y). * exact (to_enrichment_path_inv_right x y). - abstract (intros x ; cbn ; exact (pr12 F₁ x)). - abstract (intros x y z ; cbn ; exact (pr122 F₁ x y z)). - abstract (intros x y f ; cbn ; exact (!(pr222 F₁ x y f))). - abstract (intros x y f ; cbn ; use (invmaponpathsweq (make_weq _ (isweq_enriched_from_arr E₂ x y))) ; cbn ; rewrite !(enriched_from_to_arr E₂) ; refine (pr222 F₁ x y (enriched_to_arr (pr1 E₁) f) @ _) ; apply maponpaths_2 ; rewrite !(enriched_from_to_arr E₁) ; 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.