Lemma monad_to_monoid_CAT_laws : monoid_laws (monendocat_monoidal C) monad_to_monoid_CAT_data. Proof. split3; 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. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Require Import UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary. Require Import UniMath.CategoryTheory.Monads.Monads.