Lemma pre_whisker_identity (A B : precategory_data) (C : category) (H : functor_data A B) (G : functor_data B C) : pre_whisker H (nat_trans_id G) = nat_trans_id (functor_composite_data H G). Proof. apply nat_trans_eq. - apply homset_property. - intro a. apply idpath. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory.