On the Dualizability of Fusion 2-Categories
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913572928356352 |
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| author | Décoppet, Thibault D. |
| author_facet | Décoppet, Thibault D. |
| contents | Over an arbitrary field, we prove that the relative 2-Deligne tensor product of two separable module 2-categories over a compact semisimple tensor 2-category exists. This allows us to consider the Morita 4-category of compact semisimple tensor 2-categories, separable bimodule 2-categories, and their morphisms. Categorifying a result of arXiv:1312.7188, we prove that separable compact semisimple tensor 2-categories are fully dualizable objects therein. In particular, it then follows from the main theorem of arXiv:2211.04917 that, over an algebraically closed field of characteristic zero, every fusion 2-category is a fully dualizable object of the above Morita 4-category. We explain how this can be extended to any field of characteristic zero. Finally, we discuss the field theoretic interpretation of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16827 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Dualizability of Fusion 2-Categories Décoppet, Thibault D. Category Theory Quantum Algebra 16D90, 18M20, 18N25, 55U30 Over an arbitrary field, we prove that the relative 2-Deligne tensor product of two separable module 2-categories over a compact semisimple tensor 2-category exists. This allows us to consider the Morita 4-category of compact semisimple tensor 2-categories, separable bimodule 2-categories, and their morphisms. Categorifying a result of arXiv:1312.7188, we prove that separable compact semisimple tensor 2-categories are fully dualizable objects therein. In particular, it then follows from the main theorem of arXiv:2211.04917 that, over an algebraically closed field of characteristic zero, every fusion 2-category is a fully dualizable object of the above Morita 4-category. We explain how this can be extended to any field of characteristic zero. Finally, we discuss the field theoretic interpretation of our results. |
| title | On the Dualizability of Fusion 2-Categories |
| topic | Category Theory Quantum Algebra 16D90, 18M20, 18N25, 55U30 |
| url | https://arxiv.org/abs/2311.16827 |