Schemes

class sage.categories.schemes.Schemes(s=None)

Bases: sage.categories.category.Category

The category of all schemes.

EXAMPLES:

sage: Schemes()
Category of schemes

Schemes can also be used to construct the category of schemes over a given base:

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

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

Todo

Make Schemes() a singleton category (and remove Schemes from the workaround in category_types.Category_over_base._test_category_over_bases()).

This is currently incompatible with the dispatching below.

TESTS:

sage: TestSuite(Schemes()).run()

Check that Hom sets of schemes are in the correct category:

sage: Schemes().Homsets().super_categories()
[Category of homsets]
super_categories()

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 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()

EXAMPLES:

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

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