English

Monoidal categories graded by crossed modules and 3-dimensional HQFTs

Geometric Topology 2023-05-30 v3 Quantum Algebra

Abstract

Given a crossed module χ\chi, we introduce χ\chi-graded monoidal categories and χ\chi-fusion categories. We use spherical χ\chi-fusion categories to construct (via the state sum method) 3-dimensional Homotopy Quantum Field Theories with target the classifying space BχB\chi of the crossed module χ\chi (which is a homotopy 2-type).

Keywords

Cite

@article{arxiv.2207.06534,
  title  = {Monoidal categories graded by crossed modules and 3-dimensional HQFTs},
  author = {Kursat Sozer and Alexis Virelizier},
  journal= {arXiv preprint arXiv:2207.06534},
  year   = {2023}
}
R2 v1 2026-06-25T00:53:49.929Z