Corpus ID: 119269075

Unitary dual functors for unitary multitensor categories

  title={Unitary dual functors for unitary multitensor categories},
  author={David Penneys},
  journal={arXiv: Quantum Algebra},
  • David Penneys
  • Published 2018
  • Mathematics
  • arXiv: Quantum Algebra
  • We classify which dual functors on a unitary multitensor category are compatible with the dagger structure in terms of groupoid homomorphisms from the universal grading groupoid to $\mathbb{R}_{>0}$ where the latter is considered as a groupoid with one object. We then prove that all unitary dual functors induce unitarily equivalent bi-involutive structures. As an application, we provide the unitary version of the folklore correspondence between shaded planar ${\rm C^*}$ algebras with finite… CONTINUE READING