Lemma lwhisker_lwhisker_CAT {A B C D : category} {F : [A, B]} {G : [B, C]} {H I : [C, D]} (α : [C, D]⟦H, I⟧) : lwhisker_CAT F (lwhisker_CAT G α) · lassociator_CAT _ _ _ = lassociator_CAT _ _ _ · lwhisker_CAT (functor_compose F G) α. Proof. apply (nat_trans_eq D); intro c. cbn. rewrite id_left; apply 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.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering.