Fully extended invertible 4D TQFTs valued in braided fusion categories form a Z/6-extension of the Witt group, so Crane-Yetter has six inequivalent point-refinements for fixed modular data.
Remarks on global dimensions of fusion categories
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We give a nontrivial lower bound for global dimension of a spherical fusion category.
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Is Crane--Yetter fully extended?
Fully extended invertible 4D TQFTs valued in braided fusion categories form a Z/6-extension of the Witt group, so Crane-Yetter has six inequivalent point-refinements for fixed modular data.