Graded manifolds and vector bundles: A functorial correspondence

Journal Article · Mon Jul 01 04:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526921· OSTI ID:5768073

Batchelor, M

A functorial correspondence between the category of graded manifolds and the category of vectors bundles is given. Given a graded manifold (X,A), a vector bundle G over X is given as a subset of the product X x A/sup 0/ where A/sup 0/ is the dual coalgebra of A. This bundle has an obvious coalgebra structure on each fiber. The correspondence is achieved by showing that the sheaf A is isomorphic as a sheaf of algebras to the sheaf of sections of the vector bundle G' dual to G.

• Research Organization: Cambridge University, Department of Pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge CB2 1SB, England
• OSTI ID: 5768073
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

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658000 -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CLASSIFICATION
FIELD THEORIES
MAPPING
MATHEMATICAL MANIFOLDS
MATHEMATICS
SUPERGRAVITY
SUPERSYMMETRY
SYMMETRY
TENSORS
TOPOLOGICAL MAPPING
TOPOLOGY
TRANSFORMATIONS
UNIFIED-FIELD THEORIES
VECTORS