On the Dualizability of Fusion 2-Categories

Abstract

Over an arbitrary field, we prove that the relative 2-Deligne tensor product of two separable module 2-categories over a compact semisimple tensor 2-category exists. This allows us to consider the Morita 4-category of compact semisimple tensor 2-categories, separable bimodule 2-categories, and their morphisms. Categorifying a result of arXiv:1312.7188, we prove that separable compact semisimple tensor 2-categories are fully dualizable objects therein. In particular, it then follows from the main theorem of arXiv:2211.04917 that, over an algebraically closed field of characteristic zero, every fusion 2-category is a fully dualizable object of the above Morita 4-category. We explain how this can be extended to any field of characteristic zero. Finally, we discuss the field theoretic interpretation of our results.

Minor corrections

References in corpus (9)

• Fusion 2-categories and a state-sum invariant for 4-manifolds
• On the Classification of Topological Field Theories
• Minimal nondegenerate extensions
• On dualizable objects in monoidal bicategories, framed surfaces and the Cobordism Hypothesis
• Rigid and Separable Algebras in Fusion 2-Categories
• The Morita Theory of Fusion 2-Categories
• (3+1)D topological orders with only a ${\mathbb{Z}}_2$-charged particle
• Compact Semisimple 2-Categories
• Local Modules in Braided Monoidal 2-Categories

Cited by in corpus (3)

• Boundary SymTFT
• Fusion 3-Categories for Duality Defects
• Compact Semisimple Tensor 2-Categories are Morita Connected