Definition is_univalent_category_binproduct : is_univalent (category_binproduct C D). Proof. intros x y. use weqhomot. - exact (category_binproduct_z_iso_weq x y ∘ weqdirprodf (make_weq _ (HC _ _)) (make_weq _ (HD _ _)) ∘ pathsdirprodweq)%weq. - abstract (intro p ; induction p ; use subtypePath ; [ intro ; apply isaprop_is_z_isomorphism | ] ; cbn ; 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.