Fusion category

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