Definition indexed_cat_comp_nat_z_iso {C : category} (F : indexed_cat C) {x y z : C} (f : x --> y) (g : y --> z) : nat_z_iso ((F $ f) ∙ (F $ g)) (F $ (f · g)). Proof. use make_nat_z_iso. - exact (indexed_cat_comp F f g). - intro. apply is_z_isomorphism_indexed_cat_comp. 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.