proposition: Lemma is_inverse_epsinv (T : KleisliMonad C) : is_inverse_in_precat (eps_morph T : category_Kleisli C ⟦T, kleislify (unkleislify T)⟧) (epsinv_morph T).
proof: Proof. split. - apply Kleisli_Mor_eq. apply funextsec. intro a. simpl. unfold eps. apply id_left. - apply Kleisli_Mor_eq. apply funextsec. intro a. simpl. unfold eps. apply id_left. 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