proposition: Lemma ptdlaxcommutator_genopt_unit : relativelaxcommutator_unit Mon_endo_CAT Mon_ptdendo_CAT (forget_monoidal_pointed_objects_monoidal Mon_endo_CAT) ptdlaxcommutator_genopt_data.
proof: Proof. apply nat_trans_eq_alt; intro c; simpl. unfold δ_genoption_mor, BinCoproduct_of_functors_ob, BinCoproduct_of_functors_mor, BinCoproductOfArrows; simpl. repeat rewrite id_left. repeat rewrite id_right. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Combinatorics.Lists UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Chains.All UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.Colimits UniMath.CategoryTheory.Categories.HSET.Structures UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.ConstructionOfActegoryMorphisms UniMath.CategoryTheory.Actegories.CoproductsInActegories UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Monoidal.Examples.MonadsAsMonoidsElementary UniMath.CategoryTheory.DisplayedCats.Total UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.SignatureExamples UniMath.SubstitutionSystems.SumOfSignatures UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.SubstitutionSystems UniMath.SubstitutionSystems.LiftingInitial_alt UniMath.SubstitutionSystems.MonadsFromSubstitutionSystems UniMath.SubstitutionSystems.BindingSigToMonad UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems UniMath.SubstitutionSystems.ConstructionOfGHSS UniMath.SubstitutionSystems.SigmaMonoids UniMath.SubstitutionSystems.Notation