Drinfeld center of enriched monoidal categories

Abstract

We define the Drinfeld center of a monoidal category enriched over a braided monoidal category, and show that every modular tensor category can be realized in a canonical way as the Drinfeld center of a self-enriched monoidal category. We also give a generalization of this result for important applications in physics.

13 pages, a significant revision, more details are added, the final version

References in corpus (4)

• Gapless edges of 2d topological orders and enriched monoidal categories
• Extended TQFT arising from enriched multi-fusion categories
• Bicommutant categories from conformal nets
• Monoidal categories enriched in braided monoidal categories

Cited by in corpus (17)

• 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
• Categories of quantum liquids I
• One dimensional gapped quantum phases and enriched fusion categories
• A topological phase transition on the edge of the 2d ${\mathbb{Z}}_2$ topological order
• Composing topological domain walls and anyon mobility
• Pointed Drinfeld center functor
• Enriched string-net models and their excitations
• Quantum Current and Holographic Categorical Symmetry
• Extended TQFT arising from enriched multi-fusion categories
• Enriched monoidal categories I: centers
• Categorical descriptions of one-dimensional gapped phases with Abelian onsite symmetries
• Simplicity condition and boundary-bulk duality
• Bimonoidal Categories, $E_n$-Monoidal Categories, and Algebraic $K$-Theory
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes