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Frobenius algebras are finite-dimensional algebras together with a compatible inner product. Commutative Frobenius algebras have attracted recent interest because they're equivalent to 2D oriented TQFTs.
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Does every Frobenius algebra in a monoidal *-category give a Q-system?
This is a comment on Noah's answer, posted as an answer due to lack of reputation. The semion MTC is inequivalent to Vec(Z/2) as a fusion category; it is the other rank two fusion category. Confusingl …