Extended TQFT arising from enriched multi-fusion categories

Abstract

We define a symmetric monoidal (4,3)-category with duals whose objects are certain enriched multi-fusion categories. For every modular tensor category $\mathcal{C}$, there is a self enriched multi-fusion category $\mathfrak{C}$ giving rise to an object of this symmetric monoidal (4,3)-category. We conjecture that the extended 3D TQFT given by the fully dualizable object $\mathfrak{C}$ extends the 1-2-3-dimensional Reshetikhin-Turaev TQFT associated to the modular tensor category $\mathcal{C}$ down to dimension zero.

15 pages, 7 figures, comments are welcome

References in corpus (6)

• On the Classification of Topological Field Theories
• Turaev-Viro invariants as an extended TQFT
• Drinfeld center of enriched monoidal categories
• Bicommutant categories from conformal nets
• Monoidal categories enriched in braided monoidal categories
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Cited by in corpus (8)

• Boundary-bulk relation in topological orders
• A mathematical theory of gapless edges of 2d topological orders. Part I
• Gapless edges of 2d topological orders and enriched monoidal categories
• A mathematical theory of gapless edges of 2d topological orders. Part II
• A topological phase transition on the edge of the 2d ${\mathbb{Z}}_2$ topological order
• Drinfeld center of enriched monoidal categories
• Pointed Drinfeld center functor
• Enriched monoidal categories I: centers