Definition functor_to_kleisli_cat_incl_nat_z_iso {C : category} (m : Monad C) : nat_z_iso (kleisli_incl m) (Left_Kleisli_functor m ∙ functor_to_kleisli_cat m). Proof. use make_nat_z_iso. - exact (functor_to_kleisli_cat_incl_nat_trans m). - intro. use is_z_iso_kleisli_cat. apply is_z_isomorphism_identity. 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.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.EilenbergMoore. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.KleisliCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecompEquivalence.