Package sage :: Package categories :: Module category :: Class Category

Class Category

                      object --+    
                               |    
structure.sage_object.SageObject --+
                                   |
                                  Category

Known Subclasses:: category_types.Category_uniq, category_types.Category_in_ambient, category_types.Category_over_base, category_types.Elements, category_types.GSets, category_types.Groupoid, category_types.Sequences


The base class for all categories.

Instance Methods

[hide private]

__init__(self, s=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature source code

__call__(self, x)

source code

_call_(self, x)

source code

_repr_(self)

source code

_latex_(self)

source code

__hash__(self)
hash(x)

source code

short_name(self)

source code

__contains__(self, x)

source code

is_abelian(self)

source code

is_subcategory(self, c)
Returns True if self is naturally embedded as a subcategory of c.

source code

_is_subclass(self, c)

source code

__eq__(self, c)

source code

_parameters(self)

source code

category(self)
File: sage/structure/sage_object.pyx (starting at line 200)

source code

Inherited from structure.sage_object.SageObject: __new__, __repr__, _axiom_, _axiom_init_, _gap_, _gap_init_, _gp_, _gp_init_, _interface_, _interface_init_, _interface_is_cached_, _kash_, _kash_init_, _macaulay2_, _macaulay2_init_, _magma_, _magma_init_, _maple_, _maple_init_, _mathematica_, _mathematica_init_, _maxima_, _maxima_init_, _octave_, _octave_init_, _pari_, _pari_init_, _r_init_, _sage_, _singular_, _singular_init_, db, dump, dumps, plot, rename, reset_name, save, version

Inherited from object: __delattr__, __getattribute__, __reduce__, __reduce_ex__, __setattr__, __str__

Properties

[hide private]

Inherited from object: __class__

Method Details

[hide private]

init(self, s=`['4ti2-20061025',` `'R-2.6.0',` `'atlas-3.7.37',` `'atlas-3.8.1',` `'a...`)
(Constructor)

source code

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: object.__init__: (inherited documentation)

hash(self)
(Hashing function)

source code

hash(x)

Overrides: structure.sage_object.SageObject.__hash__: (inherited documentation)

is_subcategory(self, c)

source code


Returns True if self is naturally embedded as a subcategory of c.

EXAMPLES:
    sage: Rings  = Rings()
    sage: AbGrps = AbelianGroups()
    sage: Rings.is_subcategory(AbGrps)
    True
    sage: AbGrps.is_subcategory(Rings)
    False

The \code{is_subcategory} function takes into account the base.
    sage: M3 = VectorSpaces(FiniteField(3))
    sage: M9 = VectorSpaces(FiniteField(9, 'a'))
    sage: M3.is_subcategory(M9)
    False

category(self)

source code

File: sage/structure/sage_object.pyx (starting at line 200)

Overrides: structure.sage_object.SageObject.category: (inherited documentation)

Class Category

__init__(self, s=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) (Constructor)

__hash__(self) (Hashing function)

is_subcategory(self, c)

category(self)

init(self, s=`['4ti2-20061025',` `'R-2.6.0',` `'atlas-3.7.37',` `'atlas-3.8.1',` `'a...`)
(Constructor)

hash(self)
(Hashing function)