G-Sets

class sage.categories.g_sets.GSets(G)

Bases: Category

The category of \(G\)-sets, for a group \(G\).

EXAMPLES:

Sage

sage: S = SymmetricGroup(3)                                                     # needs sage.groups
sage: GSets(S)                                                                  # needs sage.groups
Category of G-sets for Symmetric group of order 3! as a permutation group

Python

>>> from sage.all import *
>>> S = SymmetricGroup(Integer(3))                                                     # needs sage.groups
>>> GSets(S)                                                                  # needs sage.groups
Category of G-sets for Symmetric group of order 3! as a permutation group

TODO: should this derive from Category_over_base?

classmethod an_instance()

Returns an instance of this class.

EXAMPLES:

Sage

sage: GSets.an_instance()  # indirect doctest                               # needs sage.groups
Category of G-sets for Symmetric group of order 8! as a permutation group

Python

>>> from sage.all import *
>>> GSets.an_instance()  # indirect doctest                               # needs sage.groups
Category of G-sets for Symmetric group of order 8! as a permutation group

super_categories()

EXAMPLES:

Sage

sage: GSets(SymmetricGroup(8)).super_categories()                           # needs sage.groups
[Category of sets]

Python

>>> from sage.all import *
>>> GSets(SymmetricGroup(Integer(8))).super_categories()                           # needs sage.groups
[Category of sets]