The Classification of Fusion 2-Categories
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913575248855040 |
|---|---|
| author | Décoppet, Thibault D. Huston, Peter Johnson-Freyd, Theo Nikshych, Dmitri Penneys, David Plavnik, Julia Reutter, David Yu, Matthew |
| author_facet | Décoppet, Thibault D. Huston, Peter Johnson-Freyd, Theo Nikshych, Dmitri Penneys, David Plavnik, Julia Reutter, David Yu, Matthew |
| contents | We classify (multi)fusion 2-categories in terms of braided fusion categories and group cohomological data. This classification is homotopy coherent -- we provide an equivalence between the 3-groupoid of (multi)fusion 2-categories up to monoidal equivalences and a certain 3-groupoid of commuting squares of $\mathrm{B}\mathbb{Z}/2$-equivariant spaces. Rank finiteness and Ocneanu rigidity for fusion 2-categories are immediate corollaries of our classification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Classification of Fusion 2-Categories Décoppet, Thibault D. Huston, Peter Johnson-Freyd, Theo Nikshych, Dmitri Penneys, David Plavnik, Julia Reutter, David Yu, Matthew Category Theory Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra 16D90, 18N10, 18M20, 18N10 We classify (multi)fusion 2-categories in terms of braided fusion categories and group cohomological data. This classification is homotopy coherent -- we provide an equivalence between the 3-groupoid of (multi)fusion 2-categories up to monoidal equivalences and a certain 3-groupoid of commuting squares of $\mathrm{B}\mathbb{Z}/2$-equivariant spaces. Rank finiteness and Ocneanu rigidity for fusion 2-categories are immediate corollaries of our classification. |
| title | The Classification of Fusion 2-Categories |
| topic | Category Theory Strongly Correlated Electrons High Energy Physics - Theory Quantum Algebra 16D90, 18N10, 18M20, 18N10 |
| url | https://arxiv.org/abs/2411.05907 |