| Title:
|
The Morita Theory of Fusion 2-Categories (English) |
| Author:
|
Décoppet, Thibault D. |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
7 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
234-292 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We develop the Morita theory of fusion 2-categories. In order to do so, we begin by proving that the relative tensor product of modules over a separable algebra in a fusion 2-category exists. We use this result to construct the Morita 3-category of separable algebras in a fusion 2-category. Then, we go on to explain how module 2-categories form a 3-category. After that, we define separable module 2-categories over a fusion 2-category, and prove that the Morita 3-category of separable algebras is equivalent to the 3-category of separable module 2-categories. As a consequence, we show that the dual tensor 2-category with respect to a separable module 2-category, that is the associated 2-category of module 2-endofunctors, is a multifusion 2-category. Finally, we give three equivalent characterizations of Morita equivalence between fusion 2-categories. (English) |
| Keyword:
|
Fusion 2-Category |
| Keyword:
|
Morita Equivalence |
| Keyword:
|
Dual Tensor 2-Category |
| Keyword:
|
Morita 3-Category |
| Keyword:
|
Separable Module 2-Category |
| MSC:
|
16D90 |
| MSC:
|
18M20 |
| MSC:
|
18M30 |
| MSC:
|
18N10 |
| MSC:
|
18N20 |
| MSC:
|
18N25 |
| idZBL:
|
Zbl 1534.18006 |
| idMR:
|
MR4600461 |
| DOI:
|
10.21136/HS.2023.07 |
| . |
| Date available:
|
2026-03-13T10:16:14Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153462 |
| . |
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