proposition: Lemma monad_to_monoid_mor_laws : pr2 (monad_to_monoid M) -->[ pr1 f] pr2 (monad_to_monoid N).
proof: Proof. split. - red. rewrite (bifunctor_equalwhiskers M_ENDO). apply (nat_trans_eq C); intro c. apply pathsinv0, Monad_Mor_μ. - apply (nat_trans_eq C); intro c. apply Monad_Mor_η. Qed.
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