Lemma is_precategory_precategory_monoid_data : is_precategory precategory_monoid_data. Proof. repeat split; intros; simpl; apply monoid_mor_eq. - apply id_left. - apply id_right. - apply assoc. - apply assoc'. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored.