Lemma Right_Kleisli_is_functor {C : category} (T : Monad C) : is_functor (Right_Kleisli_functor_data T). Proof. use tpair. - intro a. unfold Right_Kleisli_functor_data; unfold identity; unfold functor_on_morphisms; cbn. apply bind_η. - intros a b c f g; cbn. apply pathsinv0. apply bind_bind. 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.