In mathematics, a fusion category is a category that is rigid, semisimple, -linear, monoidal and has only finitely many isomorphism classes of simple objects, such that the monoidal unit is simple. If the ground field  is algebraically closed, then the latter is equivalent to  by Schur's lemma.

Examples

 Representation Category of a finite group

Reconstruction

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

References

Category theory