CW Complexes¶
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class
sage.categories.cw_complexes.
CWComplexes
(s=None)¶ Bases:
sage.categories.category_singleton.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
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Compact_extra_super_categories
()¶ 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
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class
Connected
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom
The category of connected CW complexes.
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class
ElementMethods
¶ Bases:
object
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dimension
()¶ Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: X.an_element().dimension() 2
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class
Finite
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom
Category of finite CW complexes.
A finite CW complex is a CW complex with a finite number of cells.
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class
ParentMethods
¶ Bases:
object
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dimension
()¶ Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: X.dimension() 2
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extra_super_categories
()¶ 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]
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class
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class
FiniteDimensional
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom
Category of finite dimensional CW complexes.
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class
ParentMethods
¶ Bases:
object
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cells
()¶ 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,))]
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dimension
()¶ Return the dimension of
self
.EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: X = CWComplexes().example() sage: X.dimension() 2
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class
SubcategoryMethods
¶ Bases:
object
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Connected
()¶ 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
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FiniteDimensional
()¶ 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
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super_categories
()¶ EXAMPLES:
sage: from sage.categories.cw_complexes import CWComplexes sage: CWComplexes().super_categories() [Category of topological spaces]
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