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BIRS Workshop Lecture Videos

Witt group of modular categories Davydov, Alexei


Modular categories (or non-degenerate braided fusion categories) can be thought of as generalisations of quadratic spaces. All essential features of the theory of quadratic spaces have analogues for modular categories. In particular it is possible to define Witt equivalence for modular categories. Witt classes form a group. This group is a convenient tool for classifying modular categories. Higher category structure of defects in 3d TFTs and 2d RCFTs indicate to the existence of a 3-category with modular categories as objects. This 3-category provides a higher categorification of the Witt group of modular categories.

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