Uniqueness of unitary structure for unitarizable fusion categories

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.

14 pages; v2: generalized main theorem to semisimple C*-tensor categories with possibly infinitely many simple objects

References in corpus (2)

• Fusion 2-categories and a state-sum invariant for 4-manifolds
• The tricategory of formal composites and its strictification

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