In mathematics, a fusion category is a category that is rigid, semisimple, -linear, monoidal 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

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.


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