Tannaka-Krein duality for finite 2-groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915401950035968 |
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| author | Huang, Mo Zhang, Zhi-Hao |
| author_facet | Huang, Mo Zhang, Zhi-Hao |
| contents | Let $\mathcal{G}$ be a finite 2-group. We show that the 2-category $2\mathrm{Rep}(\mathcal{G})$ of finite semisimple 2-representations is a symmetric fusion 2-category. We also relate the auto-equivalence 2-group of the symmetric monoidal forgetful 2-functor $ω: 2\mathrm{Rep}(\mathcal{G}) \to 2\mathrm{Vec}$ to the auto-equivalence 2-group of the regular algebra and show that they are equivalent to $\mathcal{G}$. This result categorifies the usual Tannaka-Krein duality for finite groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_18151 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tannaka-Krein duality for finite 2-groups Huang, Mo Zhang, Zhi-Hao Quantum Algebra Category Theory Representation Theory Let $\mathcal{G}$ be a finite 2-group. We show that the 2-category $2\mathrm{Rep}(\mathcal{G})$ of finite semisimple 2-representations is a symmetric fusion 2-category. We also relate the auto-equivalence 2-group of the symmetric monoidal forgetful 2-functor $ω: 2\mathrm{Rep}(\mathcal{G}) \to 2\mathrm{Vec}$ to the auto-equivalence 2-group of the regular algebra and show that they are equivalent to $\mathcal{G}$. This result categorifies the usual Tannaka-Krein duality for finite groups. |
| title | Tannaka-Krein duality for finite 2-groups |
| topic | Quantum Algebra Category Theory Representation Theory |
| url | https://arxiv.org/abs/2305.18151 |