Lemma monoid_to_monad_mor_laws : Monad_Mor_laws (pr1 f : monoid_to_monad M ⟹ monoid_to_monad N). 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.
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.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.CategoryTheory.Monads.Monads.