| Title:
|
Parallel transport in principal 2-bundles (English) |
| Author:
|
Waldorf, Konrad |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
2 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
57-115 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A nice differential-geometric framework for (non-abelian) higher gauge theory is provided by principal 2-bundles, i.e. categorified principal bundles. Their total spaces are Lie groupoids, local trivializations are kinds of Morita equivalences, and connections are Lie-2-algebra-valued 1-forms. In this article, we construct explicitly the parallel transport of a connection on a principal 2-bundle. 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. (English) |
| Keyword:
|
Gerbes |
| Keyword:
|
2-bundle |
| Keyword:
|
Lie groupoids |
| Keyword:
|
parallel transport |
| MSC:
|
22A22 |
| MSC:
|
53C08 |
| MSC:
|
55R65 |
| MSC:
|
58H05 |
| idZBL:
|
Zbl 1432.53030 |
| idMR:
|
MR3917427 |
| DOI:
|
10.21136/HS.2018.04 |
| . |
| Date available:
|
2026-03-10T15:53:54Z |
| Last updated:
|
2026-03-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153403 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
