proposition: Lemma is_precategory_precategory_binproduct_data : is_precategory (precategory_binproduct_data C D).
proof: Proof. repeat split; intros. - apply dirprodeq; apply id_left. - apply dirprodeq; apply id_right. - apply dirprodeq; apply assoc. - apply dirprodeq; apply assoc'. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.opp_precat