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arXiv · 1303.4663

Local Theory for 2-Functors on Path 2-Groupoids

Urs Schreiber·Konrad Waldorf
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Abstract

In this article we discuss local aspects of 2-functors defined on the path 2-groupoid of a smooth manifold; in particular, local trivializations and descent data. This is a contribution to a project that provides an axiomatic formulation of connections on (possibly non-abelian) gerbes in terms of 2-functors. The main result of this paper establishes the first part of this formulation: we prove an equivalence between the globally defined 2-functors and their locally defined descent data. The second part appears in a separate publication; there we prove equivalences between descent data, on one side, and various existing versions of gerbes with connection on the other side.

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BibTeXRIS

Urs Schreiber, Konrad Waldorf. 2013-03-19. Local Theory for 2-Functors on Path 2-Groupoids. https://doi.org/10.1007/s40062-016-0140-4

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