Schemes

sage.categories.schemes.Schemes(X=None)

Construct a category of schemes.

EXAMPLES:

sage: Schemes()
Category of Schemes

sage: Schemes(Spec(ZZ))
Category of schemes over Spectrum of Integer Ring

sage: Schemes(ZZ)
Category of schemes over Spectrum of Integer Ring

class sage.categories.schemes.Schemes_abstract

Bases: sage.categories.category.Category

The category of all abstract schemes.

EXAMPLES:

sage: Schemes()
Category of Schemes

class HomCategory(category, name=None)

Bases: sage.categories.category.HomCategory

ParentMethods

alias of HomCategory.ParentMethods

extra_super_categories()

EXAMPLES:

sage: Schemes().hom_category().extra_super_categories()
[]
sage: Schemes().hom_category().super_categories()
[Category of hom sets in Category of sets]

FIXME: what category structure is there on Homsets of schemes? The result above is wrong, and should be fixed during the next homsets overhaul.

Schemes_abstract.super_categories(*args, **kwds)

EXAMPLES:

sage: Schemes().super_categories()
[Category of sets]

class sage.categories.schemes.Schemes_over_base(base, name=None)

Bases: sage.categories.category_types.Category_over_base

The category of schemes over a given base scheme.

EXAMPLES:

sage: Schemes(Spec(ZZ))
Category of schemes over Spectrum of Integer Ring

TESTS:

sage: C = Schemes(ZZ)
sage: TestSuite(C).run()

base_scheme()

EXAMPLES:

sage: Schemes(Spec(ZZ)).base_scheme()
Spectrum of Integer Ring

super_categories(*args, **kwds)

EXAMPLES:

sage: Schemes(Spec(ZZ)).super_categories()
[Category of Schemes]