Bases: sage.categories.category_types.Category_over_base
The category of modular abelian varieties over a given field.
EXAMPLES:
sage: ModularAbelianVarieties(QQ)
Category of modular abelian varieties over Rational Field
Bases: sage.categories.homsets.HomsetsCategory
TESTS:
sage: from sage.categories.covariant_functorial_construction import CovariantConstructionCategory
sage: class FooBars(CovariantConstructionCategory):
... _functor_category = "FooBars"
sage: Category.FooBars = lambda self: FooBars.category_of(self)
sage: C = FooBars(ModulesWithBasis(ZZ))
sage: C
Category of foo bars of modules with basis over Integer Ring
sage: C.base_category()
Category of modules with basis over Integer Ring
sage: latex(C)
\mathbf{FooBars}(\mathbf{ModulesWithBasis}_{\Bold{Z}})
sage: import __main__; __main__.FooBars = FooBars # Fake FooBars being defined in a python module
sage: TestSuite(C).run()
Bases: sage.categories.category_with_axiom.CategoryWithAxiom
TESTS:
sage: C = Sets.Finite(); C
Category of finite sets
sage: type(C)
<class 'sage.categories.finite_sets.FiniteSets_with_category'>
sage: type(C).__base__.__base__
<class 'sage.categories.category_with_axiom.CategoryWithAxiom_singleton'>
sage: TestSuite(C).run()
Implement the fact that an endset of modular abelian variety is a ring.
EXAMPLES:
sage: ModularAbelianVarieties(QQ).Endsets().extra_super_categories()
[Category of rings]
EXAMPLES:
sage: ModularAbelianVarieties(QQ).base_field()
Rational Field
EXAMPLES:
sage: ModularAbelianVarieties(QQ).super_categories()
[Category of sets]