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arXiv · 2511.04482

Pivotal Brauer-Picard groupoids and graded extensions

Agustina Czenky·David Jaklitsch·Dmitri Nikshych·Julia Plavnik·David Reutter·Sean Sanford·Harshit Yadav
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Abstract

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.

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Agustina Czenky, David Jaklitsch, Dmitri Nikshych, Julia Plavnik, David Reutter, Sean Sanford, Harshit Yadav. 2025-11-06. Pivotal Brauer-Picard groupoids and graded extensions. https://arxiv.org/abs/2511.04482

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