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Title: On dualizability of braided tensor categories
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 multi-fusion categories is 4-dualizable. Via the cobordism hypothesis, this produces respectively two-, three- and four-dimensional framed local topological field theories. In particular, we produce a framed three-dimensional local topological field theory attached to the category of representations of a quantum group at any value of $q$ .  more » « less
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Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Compositio Mathematica
Page Range / eLocation ID:
435 to 483
Medium: X
Sponsoring Org:
National Science Foundation
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