Lemma monoid_to_category_ob_is_precategory : is_precategory_one_assoc monoid_to_category_ob_data. Proof. repeat split. - intros a b f. apply runax. - intros a b f. apply lunax. - intros t t' t'' t''' f g h. apply assocax. 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.