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math.CT2024
Fiber 2-Functors and Tambara-Yamagami Fusion 2-Categories
Thibault D. Décoppet, Matthew Yu
We introduce group-theoretical fusion 2-categories, a strong categorification of the notion of a group-theoretical fusion 1-category. Physically speaking, such fusion 2-categories…
math.CT2024
Extension Theory and Fermionic Strongly Fusion 2-Categories (with an Appendix by Thibault Didier Décoppet and Theo Johnson-Freyd)
Thibault Didier Décoppet
We study group graded extensions of fusion 2-categories. As an application, we obtain a homotopy theoretic classification of fermionic strongly fusion 2-categories. We examine vari…
math.CT2024
On the Dualizability of Fusion 2-Categories
Thibault D. Décoppet
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…