Definition isBinProduct_eilenberg_moore_cat : isBinProduct _ x y p π₁ π₂. Proof. use make_isBinProduct. intros w f g. use iscontraprop1. - exact (isBinProduct_eilenberg_moore_cat_unique f g). - simple refine (_ ,, _ ,, _). + exact (isBinProduct_eilenberg_moore_cat_mor f g). + exact (isBinProduct_eilenberg_moore_cat_pr1 f g). + exact (isBinProduct_eilenberg_moore_cat_pr2 f g). 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.