Definition to_adjequiv_disp_nat_trans : disp_nat_trans (nat_z_iso_id (functor_identity C)) χ₁ χ₂. Proof. simple refine (_ ,, _). - exact (λ (x : C) (xx : disp_cat_of_types C x), τ x xx). - abstract (intros x y f xx yy ff ; use eq_cod_mor ; refine (maponpaths pr1 (disp_nat_trans_ax τ ff) @ _) ; refine (transportb_cod_disp _ _ _ @ _ @ !(transportb_cod_disp _ _ _)) ; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodFunctor. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq. Require Import UniMath.CategoryTheory.DisplayedCats.ComprehensionC. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat.DispCatTerminal. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat.FibTerminal. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat.