proposition: Lemma is_natural_eps : is_nat_trans (functor_identity (category_Kleisli C)) (functor_unkleislify ∙ functor_kleislify) eps_morph.
proof: Proof. red. simpl. intros T T' α. apply (Kleisli_Mor_eq(T := T)(T' := kleislify(unkleislify T'))). simpl. apply funextsec. intro a. unfold nat_trans_from_kleisli_mor, eps. rewrite id_left. 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