Multifusion Categories and Finite Semisimple 2-Categories

Abstract

We give a 3-universal property for the Karoubi envelope of a 2-category. Using this, we show that the 3-categories of finite semisimple 2-categories (as introduced in arXiv:1812.11933) and of multifusion categories are equivalent.

arXiv commentMinor corrections

References in corpus (5)

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• On the Classification of Topological Field Theories
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• On the Equivalence of Module Categories over a Group-Theoretical Fusion Category
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Cited by in corpus (15)

• Universal Non-Invertible Symmetries
• On Continuous 2-Category Symmetries and Yang-Mills Theory
• Gauging Noninvertible Defects: A 2-Categorical Perspective
• Q-system completion for C* 2-categories
• Rigid and Separable Algebras in Fusion 2-Categories
• Finite Semisimple Module 2-Categories
• Fusion 3-Categories for Duality Defects
• The 2-Deligne Tensor Product
• Local Modules in Braided Monoidal 2-Categories
• Compact Semisimple 2-Categories
• Q-system completion is a 3-functor
• On the Dualizability of Fusion 2-Categories
• Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd)
• Orbifold completion of 3-categories
• Compact Semisimple Tensor 2-Categories are Morita Connected