Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertible braided tensor categories   We prove that a finite braided tensor category A is invertible in the Morita
4-category BrTens of braided tensor categories if, and only if, it is
non-degenerate. This includes the case of semisimple modular tensor categories,
but also non-semisimple examples such as categories of representations of the
small quantum group at good roots of unity. Via the cobordism hypothesis, we
obtain new invertible 4-dimensional framed topological field theories, which we
regard as a non-semisimple framed version of the Crane-Yetter-Kauffman
invariants, after Freed--Teleman and Walker's construction in the semisimple
case. More generally, we characterize invertibility for E_1- and E_2-algebras
in an arbitrary symmetric monoidal oo-category, and we conjecture a similar
characterization of invertible E_n-algebras for any n. Finally, we propose the
Picard group of BrTens as a generalization of the Witt group of non-degenerate
braided fusion categories, and pose a number of open questions about it.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex