Definition indexed_cat_to_disp_cat_id_comp : disp_cat_id_comp C indexed_cat_to_disp_cat_ob_mor. Proof. split. - exact (λ x xx, indexed_cat_id Φ x xx). - exact (λ x y z f g xx yy zz ff gg, ff · #(Φ $ f) gg · indexed_cat_comp Φ g f zz). Defined.
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.OppositeCategory.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.IndexedCategories.IndexedCategory.