Definition α_functors_inv (X : functor C D)(Y : functor D E)(Z : functor E F) : nat_trans (functor_composite X (functor_composite Y Z)) (functor_composite (functor_composite X Y) Z) := nat_trans_id ((X ∙ Y) ∙ Z).
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.