Definition Kleisli_functor_left_right_compose {C : category} (T : Monad C) : (Left_Kleisli_functor T) ∙ (Right_Kleisli_functor T) = T. Proof. use functor_eq. - apply homset_property. - use functor_data_eq_from_nat_trans. + intro a; apply idpath. + intros a b f; cbn. rewrite id_right. rewrite id_left. apply bind_comp_η. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.whiskering.