Lemma is_precategory_hom : is_precategory hom_data. 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.
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.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.