proposition: Lemma precategory_LModule_axioms (C : category) : is_precategory (precategory_LModule_data C).
proof: Proof. repeat split; simpl; intros. - apply (invmap (LModule_Mor_equiv _ _ )). apply (@id_left (functor_category B C)). - apply (invmap (LModule_Mor_equiv _ _ )). apply (@id_right (functor_category B C)). - apply (invmap (LModule_Mor_equiv _ _ )). apply (@assoc (functor_category B C)). - apply (invmap (LModule_Mor_equiv _ _ )). apply (@assoc' (functor_category B C)). 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.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Monads.Monads