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]