Lemma monad_to_monoid_mor_laws : pr2 (monad_to_monoid M) -->[ pr1 f] pr2 (monad_to_monoid N). 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.
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.