proposition: Lemma eta_data_laws (T : Monad C) : @Monad_Mor_laws C (@unkleislify C (@kleislify C T)) T (eta_data T).
proof: 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.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.KTriples UniMath.CategoryTheory.catiso UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.FullyFaithful