proposition: Lemma monoid_action_cat_induced_is_morphism : ∏ x m, mor_action_ax monoid_action_cat_induced_morphism_data x m.
proof: Proof. intros x m. apply monoid_action_morphism_eq. intro x0. exact (!maponpaths (λ x, F (_ ,, x)) (action_op _ _ m (pr1 x0))). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total