Lemma functor_to_is_monoidfun : ismonoidfun functor_to_monoidfun_data. Proof. use make_ismonoidfun. - intros m m'. apply (functor_comp f). - apply (functor_id f). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Monoids. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Categories.Monoid. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.AlgebraicTheories.FundamentalTheorem.CommonUtilities.MonoidActions.