proposition: Lemma is_precategory_hom : is_precategory hom_data.
proof: Proof. apply is_precategory_one_assoc_to_two. repeat split; cbn. - intros f g. apply id2_left. - intros f g. apply id2_right. - intros f g h i. apply vassocr. Qed.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct