Fusion category

-linear, semisimple, monoidal, and rigid, and has only finitely many isomorphism classes of simple objects, such that the monoidal unit is simple.

The Representation Category of a finite group

This is because of the condition of semisimplicity which needs to be checked by the Maschke's theorem.

Under Tannaka–Krein duality, every fusion category arises as the representations of a weak Hopf algebra.

Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor (2005).

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