Fusion category

From HandWiki

In mathematics, a fusion category is a category that is rigid, semisimple, k-linear, monoidal 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 Hom(1,1)k by Schur's lemma.

Examples

Reconstruction

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