Definition indexed_cat_id_z_iso {C : category} (Φ : indexed_cat C) {x : C} (xx : Φ x) : z_iso xx ((Φ $ identity x) xx). Proof. refine (indexed_cat_id Φ x xx ,, _). apply is_z_isomorphism_indexed_cat_id. 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.