| Title:
|
Drinfeld Centre-Crossed Braided Categories (English) |
| Author:
|
Wasserman, Thomas A. |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
5 |
| Issue:
|
1 |
| Year:
|
2021 |
| Pages:
|
204-243 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce, for a symmetric fusion category $\Cal A$ with Drinfeld centre $\Cal Z(\Cal A)$, the notion of $\Cal Z(\Cal A)$-crossed braided tensor category. These are categories that are enriched over $\Cal Z(\Cal A)$ equipped with a symmetric tensor product, while being braided monoidal with respect to the usual tensor product on $\Cal Z(\Cal A)$. In the Tannakian case where $\Cal A={\bf Rep}(G)$ for a finite group $G$, the 2-category of $\Cal Z(\Cal A)$-crossed braided categories is shown to be equivalent to the 2-category of $G$-crossed braided tensor categories. A similar result is established for the super Tannakian case where $\Cal A$ is the representation category of a finite super group. (English) |
| Keyword:
|
Fusion Categories |
| Keyword:
|
Braided Categories |
| Keyword:
|
Symmetric Fusion Categories |
| MSC:
|
18D10 |
| idZBL:
|
Zbl 1493.18012 |
| idMR:
|
MR4367221 |
| DOI:
|
10.21136/HS.2021.06 |
| . |
| Date available:
|
2026-03-13T05:35:35Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153438 |
| . |
| Reference:
|
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| . |
