Definition z_iso_kleisli_cat {C : category} (m : Monad C) {x₁ x₂ : kleisli_cat m} (f : z_iso (pr1 x₁) (pr1 x₂)) : z_iso x₁ x₂. Proof. simple refine (_ ,, _). - exact (pr1 f ,, tt). - use is_iso_full_sub. exact (pr2 f). 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.