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Creators/Authors contains: "Brochier, Adrien"

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  1. ; ; (, Compositio Mathematica)
    null (Ed.)
    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 $$q$$ . 
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  2. ; ; ; (, Algebraic & Geometric Topology)
    null (Ed.)
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