Uniqueness of unitary structure for unitarizable fusion categories
Quantum Algebra
2023-01-13 v2 Category Theory
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.
Keywords
Cite
@article{arxiv.1906.09710,
title = {Uniqueness of unitary structure for unitarizable fusion categories},
author = {David Reutter},
journal= {arXiv preprint arXiv:1906.09710},
year = {2023}
}
Comments
14 pages; v2: generalized main theorem to semisimple C*-tensor categories with possibly infinitely many simple objects