Definition indexed_cat_id_nat_z_iso {C : category} (Φ : indexed_cat C) (x : C) : nat_z_iso (functor_identity (Φ x)) (Φ $ identity x). Proof. refine (indexed_cat_id Φ x ,, _). intro. 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.