Definition is_z_iso_binprod_z_iso {C D : category} {c c' : C} {d d' : D} {f : c --> c'} {g : d --> d'} (f_is_z_iso : is_z_isomorphism f) (g_is_z_iso : is_z_isomorphism g) : is_z_isomorphism (f #, g). Proof. red. exists (is_z_isomorphism_mor f_is_z_iso,,is_z_isomorphism_mor g_is_z_iso). red. split; apply dirprodeq; cbn. - apply (pr1 (pr2 f_is_z_iso)). - apply (pr1 (pr2 g_is_z_iso)). - apply (pr2 (pr2 f_is_z_iso)). - apply (pr2 (pr2 g_is_z_iso)). 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.