proposition: Lemma monoid_to_monad_mor_laws : Monad_Mor_laws (pr1 f : monoid_to_monad M ⟹ monoid_to_monad N).
proof: Proof. split. - intro c. set (t := pr12 f). apply pathsinv0. etrans. 2: { exact (eqtohomot (base_paths _ _ t) c). } rewrite (bifunctor_equalwhiskers M_ENDO). apply idpath. - intro c. set (t := pr22 f). exact (eqtohomot (base_paths _ _ t) c). 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