Lemma pre_whisker_composition (A B : precategory_data) (C : category) (H : functor_data A B) (a b c : functor_data B C) (f : nat_trans a b) (g : nat_trans b c) : pre_whisker H (nat_trans_comp _ _ _ f g) = nat_trans_comp _ _ _ (pre_whisker H f) (pre_whisker H g). Proof. apply nat_trans_eq. - apply homset_property. - intro; simpl. 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.