Lemma is_precategory_monoid_precategory_data : is_precategory monoid_precategory_data. Proof. use make_is_precategory_one_assoc. - intros a b f. use monoid_id_left. - intros a b f. use monoid_id_right. - intros a b c d f g h. use monoid_assoc. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Free_Monoids_and_Groups. Require Import UniMath.Combinatorics.Lists. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Adjunctions.Core.