Definition precatbinprod_z_iso {C D : category} {X X' : C} {Z Z' : D} (α : z_iso X X') (β : z_iso Z Z') : z_iso (X ⊗ Z) (X' ⊗ Z'). Proof. set (f := catbinprodmor α β). set (g := catbinprodmor (z_iso_inv_from_z_iso α) (z_iso_inv_from_z_iso β)). exists f. exists g. split. - apply pathsdirprod; apply z_iso_inv_after_z_iso. - apply pathsdirprod; apply z_iso_after_z_iso_inv. 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.