Vector Bundles¶
- class sage.categories.vector_bundles.VectorBundles(base_space, base_field, name=None)[source]¶
- Bases: - Category_over_base_ring- The category of vector bundles over any base space and base field. - See also - EXAMPLES: - sage: M = Manifold(2, 'M', structure='top') sage: from sage.categories.vector_bundles import VectorBundles sage: C = VectorBundles(M, RR); C Category of vector bundles over Real Field with 53 bits of precision with base space 2-dimensional topological manifold M sage: C.super_categories() [Category of topological spaces] - >>> from sage.all import * >>> M = Manifold(Integer(2), 'M', structure='top') >>> from sage.categories.vector_bundles import VectorBundles >>> C = VectorBundles(M, RR); C Category of vector bundles over Real Field with 53 bits of precision with base space 2-dimensional topological manifold M >>> C.super_categories() [Category of topological spaces] - class Differentiable(base_category)[source]¶
- Bases: - CategoryWithAxiom_over_base_ring- The category of differentiable vector bundles. - A differentiable vector bundle is a differentiable manifold with differentiable surjective projection on a differentiable base space. 
 - class Smooth(base_category)[source]¶
- Bases: - CategoryWithAxiom_over_base_ring- The category of smooth vector bundles. - A smooth vector bundle is a smooth manifold with smooth surjective projection on a smooth base space. 
 - class SubcategoryMethods[source]¶
- Bases: - object- Differentiable()[source]¶
- Return the subcategory of the differentiable objects of - self.- EXAMPLES: - sage: M = Manifold(2, 'M') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).Differentiable() Category of differentiable vector bundles over Real Field with 53 bits of precision with base space 2-dimensional differentiable manifold M - >>> from sage.all import * >>> M = Manifold(Integer(2), 'M') >>> from sage.categories.vector_bundles import VectorBundles >>> VectorBundles(M, RR).Differentiable() Category of differentiable vector bundles over Real Field with 53 bits of precision with base space 2-dimensional differentiable manifold M 
 - Smooth()[source]¶
- Return the subcategory of the smooth objects of - self.- EXAMPLES: - sage: M = Manifold(2, 'M') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).Smooth() Category of smooth vector bundles over Real Field with 53 bits of precision with base space 2-dimensional differentiable manifold M - >>> from sage.all import * >>> M = Manifold(Integer(2), 'M') >>> from sage.categories.vector_bundles import VectorBundles >>> VectorBundles(M, RR).Smooth() Category of smooth vector bundles over Real Field with 53 bits of precision with base space 2-dimensional differentiable manifold M 
 
 - base_space()[source]¶
- Return the base space of this category. - EXAMPLES: - sage: M = Manifold(2, 'M', structure='top') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).base_space() 2-dimensional topological manifold M - >>> from sage.all import * >>> M = Manifold(Integer(2), 'M', structure='top') >>> from sage.categories.vector_bundles import VectorBundles >>> VectorBundles(M, RR).base_space() 2-dimensional topological manifold M 
 - super_categories()[source]¶
- EXAMPLES: - sage: M = Manifold(2, 'M') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).super_categories() [Category of topological spaces] - >>> from sage.all import * >>> M = Manifold(Integer(2), 'M') >>> from sage.categories.vector_bundles import VectorBundles >>> VectorBundles(M, RR).super_categories() [Category of topological spaces]