Fusion category

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

References

• Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor (2005). "On Fusion Categories". Annals of Mathematics. 162 (2): 581–642. ISSN 0003-486X.