Modular abelian varieties

class sage.categories.modular_abelian_varieties.ModularAbelianVarieties(Y)

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
class Homsets(category, *args)

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()
class Endset(base_category)

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()
extra_super_categories()

Implement the fact that an endset of modular abelian variety is a ring.

EXAMPLES:

sage: ModularAbelianVarieties(QQ).Endsets().extra_super_categories()
[Category of rings]
ModularAbelianVarieties.base_field()

EXAMPLES:

sage: ModularAbelianVarieties(QQ).base_field()
Rational Field
ModularAbelianVarieties.super_categories()

EXAMPLES:

sage: ModularAbelianVarieties(QQ).super_categories()
[Category of sets]

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