Definition from_z_iso_kleisli_cat {C : category} (m : Monad C) {x₁ x₂ : kleisli_cat m} (f : z_iso x₁ x₂) : z_iso (pr111 x₁) (pr111 x₂). Proof. use make_z_iso. - exact (pr1 (pr111 f)). - exact (pr111 (inv_from_z_iso f)). - split. + exact (maponpaths (λ z, pr111 z) (z_iso_inv_after_z_iso f)). + exact (maponpaths (λ z, pr111 z) (z_iso_after_z_iso_inv 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.