Definition category_binproduct_z_iso_map : z_iso (pr1 x) (pr1 y) × z_iso (pr2 x) (pr2 y) → z_iso x y. Proof. intros i. simple refine ((pr11 i ,, pr12 i) ,, _). apply is_z_iso_binprod_z_iso. - exact (pr21 i). - exact (pr22 i). 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.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat.