Abstract / Description of output
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 language | English |
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Publisher | ArXiv |
Publication status | Published - 20 Apr 2018 |
Keywords / Materials (for Non-textual outputs)
- math.QA
- math.CT
- 17B37, 18D10, 16D90, 57M27
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David Jordan
- School of Mathematics - Personal Chair of Categorical Symmetry
Person: Academic: Research Active