proposition: Lemma id_is_monoid_mor {x : C} (xx : monoid x) : is_monoid_mor xx xx (identity x).
proof: Proof. split. - refine (_ @ ! id_right _). etrans. { apply maponpaths_2, bifunctor_distributes_over_id. apply (bifunctor_leftid M). apply (bifunctor_rightid M). } apply id_left. - apply id_right. 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.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total