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()
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()
EXAMPLES:
sage: Schemes().Homsets().extra_super_categories()
[]
sage: Schemes().Homsets().super_categories()
[Category of objects]
Todo
What category structure is there on Homsets of schemes?
Todo
check that the result above is correct now
EXAMPLES:
sage: Schemes().super_categories()
[Category of sets]
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()
EXAMPLES:
sage: Schemes(Spec(ZZ)).base_scheme()
Spectrum of Integer Ring
EXAMPLES:
sage: Schemes(Spec(ZZ)).super_categories()
[Category of schemes]