Pivotal Brauer-Picard groupoids and graded extensions
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908866410708992 |
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| author | Czenky, Agustina Jaklitsch, David Nikshych, Dmitri Plavnik, Julia Reutter, David Sanford, Sean Yadav, Harshit |
| author_facet | Czenky, Agustina Jaklitsch, David Nikshych, Dmitri Plavnik, Julia Reutter, David Sanford, Sean Yadav, Harshit |
| contents | We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard $2$-categorical groups and realize them as fixed points of natural $\mathbb{Z}$ and $\mathbb{Z}/2\mathbb{Z}$ $2$-categorical actions. We classify graded extensions of a pivotal tensor category by monoidal $2$-functors into the pivotal Brauer-Picard $2$-categorical group. A similar statement is proven for spherical (unimodular) tensor categories. We also develop an obstruction theory for determining when pivotal and spherical structures can be extended. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04482 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pivotal Brauer-Picard groupoids and graded extensions Czenky, Agustina Jaklitsch, David Nikshych, Dmitri Plavnik, Julia Reutter, David Sanford, Sean Yadav, Harshit Quantum Algebra Category Theory 16T05, 18M15, 18M20 We develop pivotal and spherical versions of graded extension theory. We define the corresponding analogues of Brauer-Picard $2$-categorical groups and realize them as fixed points of natural $\mathbb{Z}$ and $\mathbb{Z}/2\mathbb{Z}$ $2$-categorical actions. We classify graded extensions of a pivotal tensor category by monoidal $2$-functors into the pivotal Brauer-Picard $2$-categorical group. A similar statement is proven for spherical (unimodular) tensor categories. We also develop an obstruction theory for determining when pivotal and spherical structures can be extended. |
| title | Pivotal Brauer-Picard groupoids and graded extensions |
| topic | Quantum Algebra Category Theory 16T05, 18M15, 18M20 |
| url | https://arxiv.org/abs/2511.04482 |