proposition: Lemma restriction_functor_ob_is_monoid_action : is_monoid_action restriction_functor_ob_monoid_action_data.
proof: Proof. use make_is_monoid_action. - intro. refine (maponpaths _ (monoidfununel f) @ _). apply (action_unel X). - intros. refine (maponpaths _ (monoidfunmul f _ _) @ _). apply (action_op X). 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