Fusion category

Summary

A fusion category is a semisimple rigid monoidal category over a field, with finite-dimensional spaces of morphisms. It has finitely many simple objects up to isomorphism, and its unit object is simple. Its structure is recorded by fusion rules: how the tensor product of two simple objects splits into simple objects. The finite-dimensional representations of a finite group over $\C$ form the basic example. Fusion categories appear in subfactor theory, in conformal field theory and in topological phases of matter.