Definition bincoproduct_obj_eilenberg_moore (x y : eilenberg_moore_cat m) : eilenberg_moore_cat m. Proof. use make_ob_eilenberg_moore. - exact (bincoproduct_obj_eilenberg_moore_ob x y). - exact (bincoproduct_obj_eilenberg_moore_ob_mor x y). - exact (bincoproduct_obj_eilenberg_moore_ob_unit x y). - exact (bincoproduct_obj_eilenberg_moore_ob_mult x y). 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.Categories.EilenbergMoore. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Preservation.