In mathematics, a fusion category is a category that is rigid, semisimple, ${\displaystyle k}$-linear, monoidal and has only finitely many isomorphism classes of simple objects, such that the monoidal unit is simple. If the ground field ${\displaystyle k}$ is algebraically closed, then the latter is equivalent to ${\displaystyle \mathrm {Hom} (1,1)\cong k}$ 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.