Parallel transport in principal 2bundles
Abstract
A nice differentialgeometric framework for (nonabelian) higher gauge theory is provided by principal 2bundles, i.e. categorified principal bundles. Their total spaces are Lie groupoids, local trivializations are kinds of Morita equivalences, and connections are Lie2algebravalued 1forms. In this article, we construct explicitly the parallel transport of a connection on a principal 2bundle. Parallel transport along a path is a Morita equivalence between the fibres over the end points, and parallel transport along a surface is an intertwiner between Morita equivalences. We prove that our constructions fit into the general axiomatic framework for categorified parallel transport and surface holonomy.
 Publication:

arXiv eprints
 Pub Date:
 April 2017
 arXiv:
 arXiv:1704.08542
 Bibcode:
 2017arXiv170408542W
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics
 EPrint:
 60 pages