fact: Definition functor_to_eilenberg_moore_cat_preserves_binproduct {C' : category} (F : C' ⟶ C) (HF : preserves_binproduct F) (α : F ∙ m ⟹ functor_identity C' ∙ F) (p₁ : ∏ (x : C'), η m (F x) · α x = identity (functor_identity C (F x))) (p₂ : ∏ (x : C'), # m (α x) · α x = μ m (F x) · α x) : preserves_binproduct (functor_to_eilenberg_moore_cat m F α p₁ p₂).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.Categories.EilenbergMoore UniMath.CategoryTheory.Subcategory.Core UniMath.CategoryTheory.Subcategory.Full UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Preservation