Lemma is_nat_trans_pre_whisker (A B C : precategory_data) (F : functor_data A B) (G H : functor_data B C) (gamma : nat_trans G H) : is_nat_trans (functor_composite_data F G) (functor_composite_data F H) (λ a : A, gamma (F a)). Proof. intros a b f; simpl. apply nat_trans_ax. 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.