proposition: Lemma forgetKleisli_faithful (C : category) : faithful (forgetfunctor_Kleisli C).
proof: Proof. intros T T'. simpl. apply isinclbetweensets. - apply isaset_total2. + apply impred_isaset. intros. apply C. + intros. apply isasetaprop. apply isaprop_Kleisli_Mor_laws. - apply isaset_nat_trans. apply C. - intros α α' p. apply Kleisli_Mor_eq. apply funextsec. intro c. change (pr1 (nat_trans_kleisli_mor α) c = pr1 (nat_trans_kleisli_mor α') c). now rewrite p. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Monads.RelativeMonads