Definition from_disp_adjequiv_enriched (F : disp_adjoint_equivalence (internal_adjoint_equivalence_identity C) E₁ E₂) : ∑ (F₁ : functor_enrichment (functor_identity _) E₁ E₂) (F₂ : functor_enrichment (functor_identity _) E₂ E₁), (nat_trans_enrichment (nat_trans_id _) (functor_id_enrichment E₁) (functor_comp_enrichment F₁ F₂)) × (nat_trans_enrichment (nat_trans_id _) (functor_comp_enrichment F₂ F₁) (functor_id_enrichment E₂)) × (nat_trans_enrichment (nat_trans_id _) (functor_comp_enrichment F₁ F₂) (functor_id_enrichment E₁)) × (nat_trans_enrichment (nat_trans_id _) (functor_id_enrichment E₂) (functor_comp_enrichment F₂ F₁)). Proof. simple refine (_ ,, _ ,, _ ,, _ ,, _ ,, _). - exact (pr1 F). - exact (pr112 F). - exact (pr1 (pr212 F)). - exact (pr2 (pr212 F)). - exact (pr11 (pr222 F)). - exact (pr12 (pr222 F)). 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.