Monoidal categories graded by crossed modules and 3-dimensional HQFTs
Geometric Topology
2023-05-30 v3 Quantum Algebra
Abstract
Given a crossed module , we introduce -graded monoidal categories and -fusion categories. We use spherical -fusion categories to construct (via the state sum method) 3-dimensional Homotopy Quantum Field Theories with target the classifying space of the crossed module (which is a homotopy 2-type).
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}
}