Definition core_disp_cat_id_comp (C : category) : disp_cat_id_comp C (core_disp_cat_ob_mor C). Proof. simple refine (_ ,, _). - intros x t. apply identity_is_z_iso. - intros x y z f g xx yy zz Hf Hg. exact (is_z_isomorphism_comp Hf Hg). 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.Groupoids. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.