Lemma is_precategory_precategory_Alg_data : is_precategory (precategory_Alg_data T). Proof. apply make_is_precategory; intros; apply Algebra_mor_eq. - apply id_left. - apply id_right. - apply assoc. - apply assoc'. Qed.
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.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.Derivative.