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# 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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