In a related question to
https://ask.sagemath.org/question/48756/do-covariant-constructions-commute-with-withbasis/
I have a category Cs which implements the axiom FinitelyGeneratedAsCs. I want to define parent methods for graded objects of Cs. Some of these apply for all objects, some only for the finitely generated ones. If I have a design sketched as
class Cs(Category_over_base_ring):
class Subcategorymethods:
def Graded(self):
return GradedModules.category_of(self)
def FinitelyGenerate(self):
return self._with_axiom("FinitelyGeneratedAsCs")
class Graded(GradedModulesCategory):
class ParentMethods:
def some_method_for_all_parents(self)
class FinitelyGeneratedAsCs(CategoryWithAxiom_over_base_ring):
class Graded(GradedModulesCategory):
class ParentMethods:
def some_method_only_for_fg_graded_parents(self):
Then I receceive
sage: Cs(QQ).FinitelyGenerated().Graded()
TypeError: Graded() takes exactly 1 argument (2 given)
If I however implement Graded as an axiom, say FakeGraded then I can set up parent methods as described above (just need to add a call to self._with_axiom('FakeGraded') in the appropriate place. I thought however that to have better integration with other parts of Sage I should implement Graded as the functorial construction in GradedModulesCategory but I'm hitting the above error.
