Lemma is_precategory_functor_precategory_data (C:precategory_data)(C' : precategory) (hs: has_homsets C'): is_precategory (functor_precategory_data C C'). Proof. apply is_precategory_one_assoc_to_two. repeat split; simpl; intros. unfold identity. simpl. apply nat_trans_eq. apply hs. intro x; simpl. apply id_left. apply nat_trans_eq. apply hs. intro x; simpl. apply id_right. apply nat_trans_eq. apply hs. intro x; simpl. apply assoc. Qed.
Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence.