Schreiber, Urs and Waldorf, Konrad (2017) Local theory for 2-functors on path 2-groupoids. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 12 (3). pp. 617-658. ISSN 2193-8407, 1512-2891
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This article is concerned with 2-functors defined on the path 2-groupoid of a smooth manifold. We set up a procedure to extract local data of such 2-functors, similar to the extraction of transition functions of a fibre bundle. The main result of this paper establishes an equivalence between the globally defined 2-functors and their local 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, of which the present paper provides the first part. The second part provides equivalences between the local data, on one side, and various existing versions of gerbes with connection on the other side.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Smooth paths; Fundamental 2-groupoid; Descent theory; Parallel transport; Non-abelian gerbes |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:15 |
| Last Modified: | 18 Feb 2019 14:32 |
| URI: | https://pred.uni-regensburg.de/id/eprint/1316 |
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