Definition Id_in_sub_to_iso (a b : ob (full_sub_category C C')): a = b -> z_iso (pr1 a) (pr1 b) := funcomp (@idtoiso _ a b) (iso_from_iso_in_sub a b).
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. 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.Subcategory.Core.