Definition Kleisli_homset_iso {C : category} (T : Monad C) : natural_hom_weq (Left_Kleisli_functor T) (Right_Kleisli_functor T). Proof. use tpair. - intros a b; cbn. apply idweq. - cbn; split. + intros. rewrite <- assoc. apply cancel_precomposition. apply η_bind. + intros; apply idpath. 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.