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• W3014579814 endingPage "2140" @default.
• W3014579814 startingPage "2107" @default.
• W3014579814 abstract "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." @default.
• W3014579814 created "2020-04-10" @default.
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• W3014579814 date "2021-08-18" @default.
• W3014579814 modified "2023-10-04" @default.
• W3014579814 title "Invertible braided tensor categories" @default.
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• W3014579814 doi "https://doi.org/10.2140/agt.2021.21.2107" @default.
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