Parallel Transport and Functors

Details Parallel Transport and Functors Parallel Transport and Functors

2007-05-03

arxiv.org/abs/0705.0452v4

J. Homotopy Relat. Struct. 4, 187-244 (2009)

Mathematics

Differential Geometry

71 pages, 1 figure. Version 2 contains several improvements, in particular concerning the proofs of Lemma 2.15 and of Proposit

Scientific paper

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.

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