proposition: Lemma Mon_alg_action_mor_rel {T : pointed} (X : Mon_alg T) {A B : C} (f : A --> B) : Mon_alg_mor_axioms (_,, Mon_alg_action_alg_map_rel X A) (_,, Mon_alg_action_alg_map_rel X B) (pr1 X ⊗^{ V}_{l} f).
proof: Proof. destruct X as [X [x xrel]]. etrans. apply assoc'. etrans. apply cancel_precomposition. use (whiskerscommutes _ (bifunctor_equalwhiskers V)). etrans. apply assoc. apply pathsinv0. etrans. apply assoc. apply cancel_postcomposition. apply (monoidal_associatorinvnatleft V). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids