proposition: Lemma is_functor_unkleislify {C : category} : is_functor (functor_data_unkleislify C).
proof: Proof. split; red; simpl; intros. - unfold unkleislify_mor. apply subtypePath; simpl. + intro. apply isaprop_disp_Monad_Mor_laws; apply homset_property. + apply subtypePath; simpl. * intro. apply isaprop_is_nat_trans; apply homset_property. * now apply funextsec. - apply subtypePath; simpl. + intro. apply isaprop_disp_Monad_Mor_laws; apply homset_property. + apply subtypePath; simpl. * intro. apply isaprop_is_nat_trans; apply homset_property. * now apply funextsec. 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