proposition: Lemma is_natural_eta : is_nat_trans (functor_composite_data (functor_data_kleislify C) (functor_data_unkleislify C)) (functor_identity (category_Monad C)) eta_morph.
proof: Proof. red; simpl. intros T T' α. apply (Monad_Mor_eq (unkleislify (kleislify T))). intros. simpl. unfold eta_arrow. now rewrite id_left, 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