Vector Bundles#
- class sage.categories.vector_bundles.VectorBundles(base_space, base_field, name=None)#
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]
- class Differentiable(base_category)#
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)#
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#
Bases:
object
- Differentiable()#
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
- Smooth()#
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
- base_space()#
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
- super_categories()#
EXAMPLES:
sage: M = Manifold(2, 'M') sage: from sage.categories.vector_bundles import VectorBundles sage: VectorBundles(M, RR).super_categories() [Category of topological spaces]