proposition: Lemma is_precategory_precategory_alg_data {C : category} (F : functor C C) : is_precategory (precategory_alg_data F).
proof: Proof. repeat split; intros; simpl. - apply algebra_mor_eq. apply id_left. - apply algebra_mor_eq. apply id_right. - apply algebra_mor_eq. apply assoc. - apply algebra_mor_eq. apply assoc'. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.NNO