On minimal non-degenerate extensions of braided tensor categories
[Moved Online] Tensor categories and topological quantum field theories March 16, 2020 - March 20, 2020
braided tensor category
higher categorical groups
extensions of tensor categories
18D10 - Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
This is a report on the joint work of Alexei Davydov and the speaker. Let B be a braided tensor category. A non-degenerate braided category M containing B is called a minimal extension if the centralizer of B in M coincides with the symmetric center of B. We will discuss the existence problem for minimal extensions. When the symmetric center is pointed, this problem can be approached using the braided Picard group of B. We compute the (higher categorical) Lan-Kong-Wen group of minimal extensions of a symmetric fusion category in this case.
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