Finite Semisimple Module 2-Categories

Abstract

Let $\mathfrak{C}$ be a multifusion 2-category. We show that every finite semisimple $\mathfrak{C}$-module 2-category is canonically enriched over $\mathfrak{C}$. Using this enrichment, we prove that every finite semisimple $\mathfrak{C}$-module 2-category is equivalent to the 2-category of modules over a rigid algebra in $\mathfrak{C}$.

arXiv commentMinor Revision

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Cited by in corpus (9)

• Boundary SymTFT
• Fiber 2-Functors and Tambara-Yamagami Fusion 2-Categories
• Fusion 3-Categories for Duality Defects
• Compact Semisimple 2-Categories
• Twisted gauging and topological sectors in (2+1)d abelian lattice gauge theories
• Local Modules in Braided Monoidal 2-Categories
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Les Houches Lecture Notes on Tensor Networks
• Compact Semisimple Tensor 2-Categories are Morita Connected