proposition: Lemma is_catiso : is_catiso (functor_unkleislify(C:=C)).
proof: Proof. split. - apply fully_faithful_from_equivalence. use (is_left_adjoint_functor_unkleislify,, form_equivalence_unkleislify). - apply (isweq_iso _ (λ T : Monad C, kleislify T)). + intro T. simpl. apply kleislify_unkleislify. + simpl. apply unkleislify_kleislify. 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