Lemma horcomp_id_prewhisker {C D E : category} (X : functor C D) (Z Z' : functor D E) (f : nat_trans Z Z') : horcomp (nat_trans_id X) f = pre_whisker _ f. Proof. apply (nat_trans_eq E); intro x; simpl; unfold horcomp_data; simpl. now rewrite functor_id, id_right. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors.