fact: Definition monad_to_monoid_mor : monad_to_monoid M --> monad_to_monoid N := pr1 f ,, monad_to_monoid_mor_laws.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal UniMath.CategoryTheory.Monads.Monads