In mathematics, a fusion category is a category that is abelian, -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 is algebraically closed, then the latter is equivalent to by Schur's lemma.
Examples
editReconstruction
editUnder Tannaka–Krein duality, every fusion category arises as the representations of a weak Hopf algebra.
References
edit- Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor (2005). "On Fusion Categories". Annals of Mathematics. 162 (2): 581–642. ISSN 0003-486X.