Lemma monad_to_monoid_laws : monoid_laws M_ENDO monad_to_monoid_data. Proof. repeat split; apply (nat_trans_eq C); intro c; cbn. - apply Monad_law2. - apply Monad_law1. - rewrite id_left. apply pathsinv0, Monad_law3. 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.