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arXiv · 1804.07538

On dualizability of braided tensor categories

Adrien Brochier·David Jordan·Noah Snyder
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Abstract

We study the question of dualizability in higher Morita categories of locally presentable tensor categories and braided tensor categories. Our main results are that the 3-category of rigid tensor categories with enough compact projectives is 2-dualizable, that the 4-category of rigid braided tensor categories with enough compact projectives is 3-dualizable, and that (in characteristic zero) the 4-category of braided fusion categories is 4-dualizable. Via the cobordism hypothesis, this produces respectively 2, 3 and 4-dimensional framed local topological field theories. In particular, we produce a framed 3-dimensional local TFT attached to the category of representations of a quantum group at any value of $q$.

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Adrien Brochier, David Jordan, Noah Snyder. 2018-04-20. On dualizability of braided tensor categories. https://doi.org/10.1112/s0010437x20007630

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