Fusion category

In mathematics, a fusion category is a category that is abelian, ${\displaystyle k}$-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 ${\displaystyle k}$ is algebraically closed, then the latter is equivalent to ${\displaystyle \mathrm {Hom} (1,1)\cong k}$ by Schur's lemma.