Definition isPullback_eilenberg_moore : isPullback q. Proof. intros w h k r. use iscontraprop1. - exact (isPullback_eilenberg_moore_unique h k). - simple refine (_ ,, _ ,, _). + exact (isPullback_eilenberg_moore_mor h k r). + abstract (use eq_mor_eilenberg_moore ; apply (PullbackArrow_PullbackPr1 (make_Pullback _ H))). + abstract (use eq_mor_eilenberg_moore ; apply (PullbackArrow_PullbackPr2 (make_Pullback _ H))). 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.