Parallel Transport and Functors
By Urs Schreiber, K. Waldorf. 2007
104 citations recorded by the source corpus.
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we introduce: local trivializations and smooth descent data. This provides a way to substitute categories of functors for categories of smooth fibre bundles with connection. We indicate that this concept can be generalized to connections in categorified bundles, and how this generalization improves the understanding of higher dimensional parallel transport.
Subfields: Mathematical Physics, Radiology, Nuclear Medicine and Imaging
View Paper: https://www.semanticscholar.org/paper/d967436da8c7558f72345c9714d273e44e505cf2
How researchers see this paper
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In Mathematical Physics
- John Huerta
- Christoph Wockel
- John C. Baez
- Bob Coecke
- A. Henriques
- Christopher J. Schommer-Pries
- J. Elgueta
- Urs Schreiber
In Radiology, Nuclear Medicine and Imaging
Citations in the corpus
- Principal 2-bundles and their gauge 2-groups (2008, background): “[46] for ordinary principal bundles and [47] for principal 2-bundles), which is closely related to our approach.”
- An invitation to higher gauge theory (2010, methodology): “For these, the reader can turn to Section 2.1 of Schreiber and Waldorf [87].”