Lemma eta_data_laws (T : Monad C) : @Monad_Mor_laws C (@unkleislify C (@kleislify C T)) T (eta_data T). Proof. split; simpl; intros. - unfold eta_arrow. rewrite id_right. rewrite id_left. unfold Monads.μ, μ, bind, μ. simpl. unfold Monads.bind, Monads.μ. rewrite functor_id. do 2 rewrite id_left. apply idpath. - apply id_right. 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.