Lemma is_nat_trans_post_whisker (B C D : precategory_data) (G H : functor_data B C) (gamma : nat_trans G H) (K : functor C D): is_nat_trans (functor_composite_data G K) (functor_composite_data H K) (λ b : B, #K (gamma b)). Proof. unfold is_nat_trans. simpl in *. intros; repeat rewrite <- functor_comp. rewrite (nat_trans_ax gamma). 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.