Any finite modular tensor category gives a 3-dimensional derived TQFT whose state spaces are derived Hom spaces, recovering known non-semisimple TQFTs after taking zeroth cohomology.
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3-dimensional TQFTs from derived categories of quantum group representations
Any finite modular tensor category gives a 3-dimensional derived TQFT whose state spaces are derived Hom spaces, recovering known non-semisimple TQFTs after taking zeroth cohomology.