Lemma pentagon_eq_of_endofunctors: pentagon_eq (functorial_composition _ _ _) associator_of_endofunctors. Proof. intros F G H I. apply nat_trans_eq_alt. intro c. cbn. do 4 rewrite id_right. do 3 rewrite functor_id. rewrite id_right. apply pathsinv0, functor_id. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats.