Lemma is_precategory_precategory_binproduct_data : is_precategory (precategory_binproduct_data C D). Proof. repeat split; intros. - apply dirprodeq; apply id_left. - apply dirprodeq; apply id_right. - apply dirprodeq; apply assoc. - apply dirprodeq; apply assoc'. 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.