Lemma is_functor_unkleislify {C : category} : is_functor (functor_data_unkleislify C). 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.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.KTriples. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful.