Definition category_binproduct_z_iso_weq : z_iso (pr1 x) (pr1 y) × z_iso (pr2 x) (pr2 y) ≃ z_iso x y. Proof. use make_weq. - exact category_binproduct_z_iso_map. - use isweq_iso. + exact category_binproduct_z_iso_inv. + abstract (intros i ; use pathsdirprod ; (use subtypePath ; [ intro ; apply isaprop_is_z_isomorphism | ]) ; apply idpath). + abstract (intros i ; use subtypePath ; [ intro ; apply isaprop_is_z_isomorphism | ] ; apply idpath). 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.