CW Complexes¶
- class sage.categories.cw_complexes.CWComplexes[source]¶
Bases:
Category_singleton
The category of CW complexes.
A CW complex is a Closure-finite cell complex in the Weak topology.
REFERENCES:
Note
The notion of “finite” is that the number of cells is finite.
EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: C = CWComplexes(); C Category of CW complexes
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> C = CWComplexes(); C Category of CW complexes
- Compact_extra_super_categories()[source]¶
Return extraneous super categories for
CWComplexes().Compact()
.A compact CW complex is finite, see Proposition A.1 in [Hat2002].
Todo
Fix the name of finite CW complexes.
EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: CWComplexes().Compact() # indirect doctest Category of finite finite dimensional CW complexes sage: CWComplexes().Compact() is CWComplexes().Finite() True
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> CWComplexes().Compact() # indirect doctest Category of finite finite dimensional CW complexes >>> CWComplexes().Compact() is CWComplexes().Finite() True
- class Connected(base_category)[source]¶
Bases:
CategoryWithAxiom
The category of connected CW complexes.
- class ElementMethods[source]¶
Bases:
object
- dimension()[source]¶
Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: X.an_element().dimension() 2
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example() >>> X.an_element().dimension() 2
- class Finite(base_category)[source]¶
Bases:
CategoryWithAxiom
Category of finite CW complexes.
A finite CW complex is a CW complex with a finite number of cells.
- class ParentMethods[source]¶
Bases:
object
- dimension()[source]¶
Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: X.dimension() 2
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example() >>> X.dimension() 2
- extra_super_categories()[source]¶
Return the extra super categories of
self
.A finite CW complex is a compact finite-dimensional CW complex.
EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: C = CWComplexes().Finite() sage: C.extra_super_categories() [Category of finite dimensional CW complexes, Category of compact topological spaces]
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> C = CWComplexes().Finite() >>> C.extra_super_categories() [Category of finite dimensional CW complexes, Category of compact topological spaces]
- class FiniteDimensional(base_category)[source]¶
Bases:
CategoryWithAxiom
Category of finite dimensional CW complexes.
- class ParentMethods[source]¶
Bases:
object
- cells()[source]¶
Return the cells of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: C = X.cells() sage: sorted((d, C[d]) for d in C.keys()) [(0, (0-cell v,)), (1, (0-cell e1, 0-cell e2)), (2, (2-cell f,))]
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example() >>> C = X.cells() >>> sorted((d, C[d]) for d in C.keys()) [(0, (0-cell v,)), (1, (0-cell e1, 0-cell e2)), (2, (2-cell f,))]
- dimension()[source]¶
Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: X.dimension() 2
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> X = CWComplexes().example() >>> X.dimension() 2
- class SubcategoryMethods[source]¶
Bases:
object
- Connected()[source]¶
Return the full subcategory of the connected objects of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: CWComplexes().Connected() Category of connected CW complexes
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> CWComplexes().Connected() Category of connected CW complexes
- FiniteDimensional()[source]¶
Return the full subcategory of the finite dimensional objects of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: C = CWComplexes().FiniteDimensional(); C Category of finite dimensional CW complexes
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> C = CWComplexes().FiniteDimensional(); C Category of finite dimensional CW complexes
- super_categories()[source]¶
EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: CWComplexes().super_categories() [Category of topological spaces]
>>> from sage.all import * >>> from sage.categories.cw_complexes import CWComplexes >>> CWComplexes().super_categories() [Category of topological spaces]