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We develop the Witt group for certain braided monoidal categories withduality. In case of a braided fusion category over an algebraically closedfield of characteristic zero, we explicitly describe this structure. We thenuse this description to prove that this tool provides an invariant for finiteisocategorical groups. As an application, we show that all groups of order lessthan 64 are categorically rigid.

The Witt group of a braided Monoidal category