A diagrammatic presentation for every pivotal pointed fusion category

Abstract

We provide a generators and relations presentation of pivotal pointed fusion categories, $Vec(G,\omega ,\pi )$. Unlike the well-known skeletal model, our presentation is strict and allows multiple isomorphic objects. Our main tool is skein theory, which allows us to apply topological tools to understand the relations of morphisms in the category. This expository paper provides details of skein-theoretic work in the setup that allows multiple isomorphic labels in the generators, which didn't previously exist in the literature.

arXiv comment10 pages. Comments are welcome