Definition category_binproduct_z_iso_inv : z_iso x y → z_iso (pr1 x) (pr1 y) × z_iso (pr2 x) (pr2 y) := λ i, functor_on_z_iso (pr1_functor C D) i ,, functor_on_z_iso (pr2_functor C D) i.
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.