proposition: Lemma monad_to_monoid_CAT_laws : monoid_laws (monendocat_monoidal C) monad_to_monoid_CAT_data.
proof: Proof. split3; apply (nat_trans_eq C); intro c; cbn. - apply Monad_law2. - apply Monad_law1. - rewrite id_left. apply pathsinv0, Monad_law3. 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.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Monads.Monads