Proposition hom_precat_laws {C : two_cat} (x y : C) : is_precategory (hom_precat_data x y). Proof. use is_precategory_one_assoc_to_two. repeat split ; cbn. - intros f g τ. apply id2_left. - intros f g τ. apply id2_right. - intros f g h k τ₁ τ₂ τ₃. apply vassocr. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.Univalence.