Definition functor_precategory_data (C : precategory_data)(C' : precategory): precategory_data. Proof. apply (make_precategory_data (functor_precategory_ob_mor C C')). + intro a; simpl. apply (nat_trans_id (pr1 a)). + intros a b c f g. apply (nat_trans_comp _ _ _ f g). Defined.
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.