Lemma form_adjunction_eps_eta : form_adjunction functor_unkleislify functor_kleislify eps_natural eta_natural. Proof. split; red; simpl. - intro T. apply (Monad_Mor_eq (unkleislify T) (unkleislify T)). intros. simpl. unfold eps. now rewrite id_left. - intro T. apply (Kleisli_Mor_eq (T:=kleislify T) (T':=kleislify T)). intros. simpl. apply funextsec. intro a. unfold eps. now rewrite id_left. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.KTriples. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful.