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.category.HomCategory
Initializes this HomCategory
EXAMPLES:
We need to skip one test, since the hierarchy of hom categories isn’t consistent yet:
sage: C = sage.categories.category.HomCategory(Rings()); C
Category of hom sets in Category of rings
sage: TestSuite(C).run(skip=['_test_category_graph'])
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.
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]