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- W4308759105 abstract "We prove that the Drinfeld center of a fusion 2-category is invariant under Morita equivalence. We go on to show that the concept of Morita equivalence between connected fusion 2-categories recovers exactly the notion of Witt equivalence between braided fusion 1-categories. A strongly fusion 2-category is a fusion 2-category whose braided fusion 1-category of endomorphisms of the monoidal unit is $mathbf{Vect}$ or $mathbf{SVect}$. We prove that every fusion 2-category is Morita equivalent to the 2-Deligne tensor product of a strongly fusion 2-category and an invertible fusion 2-category. We proceed to show that every fusion 2-category is Morita equivalent to a connected fusion 2-category. As a consequence, we find that every rigid algebra in a fusion 2-category is separable. This implies in particular that every fusion 2-category is separable. Conjecturally, separability ensures that a fusion 2-category is 4-dualizable. We define the dimension of a fusion 2-category, and prove that it is always non-zero. Finally, we show that the Drinfeld center of any fusion 2-category is a finite semisimple 2-category." @default.
- W4308759105 created "2022-11-15" @default.
- W4308759105 creator A5060752005 @default.
- W4308759105 date "2022-11-09" @default.
- W4308759105 modified "2023-09-30" @default.
- W4308759105 title "Drinfeld Centers and Morita Equivalence Classes of Fusion 2-Categories" @default.
- W4308759105 doi "https://doi.org/10.48550/arxiv.2211.04917" @default.
- W4308759105 hasPublicationYear "2022" @default.
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