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arxiv: 1412.3417 · v1 · submitted 2014-12-10 · 🧮 math.KT · math.CT

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The Witt group of a braided Monoidal category

Isar Goyvaerts , Ehud Meir
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classification 🧮 math.KT math.CT
keywords braidedcategorygroupgroupsmonoidalwittalgebraicallyapplication
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We develop the Witt group for certain braided monoidal categories with duality. In case of a braided fusion category over an algebraically closed field of characteristic zero, we explicitly describe this structure. We then use this description to prove that this tool provides an invariant for finite isocategorical groups. As an application, we show that all groups of order less than 64 are categorically rigid.

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  1. Complete Isocategorical Classification of Groups of Order 64 via GAP

    math.GR 2026-04 unverdicted novelty 7.0

    There are exactly two pairs of non-isomorphic groups of order 64 whose representation categories are monoidally equivalent.