On dualizability of braided tensor categories

Adrien Brochier, David Jordan, Noah Snyder

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)435 - 483
Number of pages70
JournalCompositio Mathematica
Volume157
Issue number3
Early online date9 Mar 2021
DOIs
Publication statusE-pub ahead of print - 9 Mar 2021

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