The 2-categorical S-matrix of a braided fusion 1-category is a character table
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909996017516544 |
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| author | Hofstetter, Alea Schweigert, Christoph |
| author_facet | Hofstetter, Alea Schweigert, Christoph |
| contents | The semisimple module categories over a braided fusion category $\mathcal{C}$ form a connected fusion 2-category $\text{Mod}(\mathcal{C})$. Its Drinfeld center $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ is a braided fusion 2-category. To any braided fusion 2-category, Johnson-Freyd and Reutter arXiv:2105.15167v3 [math.QA] have associated a matrix-valued invariant, the 2-categorical $S$-matrix. In this short note we investigate this matrix of $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ as an invariant for the braided fusion 1-category $\mathcal{C}$ and show that it reduces to the character table of the Müger center of $\mathcal{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The 2-categorical S-matrix of a braided fusion 1-category is a character table Hofstetter, Alea Schweigert, Christoph Quantum Algebra The semisimple module categories over a braided fusion category $\mathcal{C}$ form a connected fusion 2-category $\text{Mod}(\mathcal{C})$. Its Drinfeld center $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ is a braided fusion 2-category. To any braided fusion 2-category, Johnson-Freyd and Reutter arXiv:2105.15167v3 [math.QA] have associated a matrix-valued invariant, the 2-categorical $S$-matrix. In this short note we investigate this matrix of $\mathcal{Z}(\text{Mod}(\mathcal{C}))$ as an invariant for the braided fusion 1-category $\mathcal{C}$ and show that it reduces to the character table of the Müger center of $\mathcal{C}$. |
| title | The 2-categorical S-matrix of a braided fusion 1-category is a character table |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2601.14168 |