Lemma vcomp_whisker_CAT {A B C : category} {F G : [A, B]} {H I : [B, C]} (α : [A, B]⟦F, G⟧) (β : [B, C]⟦H, I⟧) : rwhisker_CAT H α · lwhisker_CAT G β = lwhisker_CAT F β · rwhisker_CAT I α. Proof. apply (nat_trans_eq C); intro c. apply (pr2 β). 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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.