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 $\mathfrak{C}$.

Minor Revision

References in corpus (7)

• Fusion 2-categories and a state-sum invariant for 4-manifolds
• Minimal nondegenerate extensions
• On dualizable objects in monoidal bicategories, framed surfaces and the Cobordism Hypothesis
• Extended 3-dimensional bordism as the theory of modular objects
• Categories of quantum liquids II
• The 2-Deligne Tensor Product
• Weak Fusion 2-Categories

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