Modular abelian varieties¶
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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
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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" ....: _base_category_class = (Category,) 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()
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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()
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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]
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class
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ModularAbelianVarieties.
base_field
()¶ EXAMPLES:
sage: ModularAbelianVarieties(QQ).base_field() Rational Field
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ModularAbelianVarieties.
super_categories
()¶ EXAMPLES:
sage: ModularAbelianVarieties(QQ).super_categories() [Category of sets]
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class