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Uniqueness of unitary structure for unitarizable fusion categories
Published 24 Jun 2019 in math.QA and math.CT | (1906.09710v2)
Abstract: We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified polar decomposition theorem for monoidal equivalences between such categories. We prove analogous results for unitarizable braided fusion categories and module categories.
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