Lemma post_whisker_identity (A B : precategory) (C : category) (H : functor B C) (G : functor_data A B) : post_whisker (nat_trans_id G) H = nat_trans_id (functor_composite_data G H). Proof. apply nat_trans_eq. - apply homset_property. - intro a. unfold post_whisker. simpl. apply functor_id. 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.