Fusion category
From HandWiki
In mathematics, a fusion category is a category that is rigid, semisimple, [math]\displaystyle{ k }[/math]-linear, monoidal and has only finitely many isomorphism classes of simple objects, such that the monoidal unit is simple. If the ground field [math]\displaystyle{ k }[/math] is algebraically closed, then the latter is equivalent to [math]\displaystyle{ \mathrm{Hom}(1,1)\cong k }[/math] by Schur's lemma.
Examples
Reconstruction
Under Tannaka-Krein duality, every fusion category arises as the representations of a weak Hopf algebra.
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