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  "body": "\n## Summary\n\nA fusion category is a semisimple [[rigid monoidal category|A10WW8GEKR]] over a field, with finite-dimensional spaces of morphisms.\nIt has finitely many simple objects up to isomorphism, and its unit object is simple.\nIts structure is recorded by fusion rules: how the tensor product of two simple objects splits into simple objects.\nThe finite-dimensional representations of a finite group over $\\C$ form the basic example.\nFusion categories appear in subfactor theory, in conformal field theory and in topological phases of matter.\n\n## Explanations\n\n### L1 human\n\nA fusion category is a finite \"multiplication table\" for building blocks that can be combined and decomposed.\nThere are finitely many basic objects, every object is a sum of basic ones, and combining two basic objects gives a sum of basic objects again.\nFor example, the group $\\Z/2$ has two irreducible complex representations, the trivial one $1$ and the sign $s$.\nTheir tensor products are $1 \\otimes 1 = 1$, $1 \\otimes s = s$ and $s \\otimes s = 1$.\n",
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