Definition adjunction_enrichment_weq {V : monoidal_cat} (E₁ E₂ : enriched_cat V) (L : adjunction (pr1 E₁) (pr1 E₂)) : disp_adjunction L (pr2 E₁) (pr2 E₂) ≃ adjunction_enrichment (adjunction_weq_adjunction_univ_cats (pr1 E₁) (pr1 E₂) L) (pr2 E₁) (pr2 E₂). Proof. use weq_iso. - exact (λ LL, pr1 LL ,, pr112 LL ,, pr1 (pr212 LL) ,, pr2 (pr212 LL)). - refine (λ LL, left_adjoint_enrichment LL ,, (right_adjoint_enrichment LL ,, (adjoint_unit_enrichment LL ,, adjoint_counit_enrichment LL)) ,, _). abstract (split ; apply disp_2cell_isapprop_enriched_cats). - abstract (intro LL ; refine (maponpaths (λ z, _ ,, z) _) ; use subtypePath ; [ intro ; apply isapropdirprod ; apply disp_cellset_property | ] ; apply idpath). - abstract (intro LL ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentAdjunction. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.UnitEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.FullSubEnriched. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInBicatOfUnivCats. Import MonoidalNotations.