Definition co_eilenberg_moore_cat_pred (f : dialgebra (functor_identity C) m) : hProp. Proof. use make_hProp. - exact (pr2 f · ε m _ = identity _ × pr2 f · δ m (pr1 f) = pr2 f · # m (pr2 f)). - apply isapropdirprod ; apply homset_property. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Monads.Comonads.