Fusion category

In mathematics, a fusion category is a category that is rigid, semisimple, formula_1-linear, monoidal and has only finitely many isomorphism classes of simple objects, such that the monoidal unit is simple. If the ground field formula_1 is algebraically closed, then the latter is equivalent to formula_3 by Schur's lemma.
Reconstruction.
Under Tannaka-Krein duality, every fusion category arises as the representations of a weak Hopf algebra.