Definition eilenberg_moore_cat_pred (f : dialgebra m (functor_identity C)) : hProp. Proof. use make_hProp. - exact (η m _ · pr2 f = identity _ × μ m (pr1 f) · pr2 f = # m (pr2 f) · 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.Monads.