# Fusion categories in terms of graphs and relations

@article{Pfeiffer2009FusionCI,
title={Fusion categories in terms of graphs and relations},
author={H. Pfeiffer},
journal={arXiv: Quantum Algebra},
year={2009}
}
• H. Pfeiffer
• Published 2009
• Mathematics, Physics
• arXiv: Quantum Algebra
• Every fusion category C that is k-linear over a suitable field k, is the category of finite-dimensional comodules of a Weak Hopf Algebra H. This Weak Hopf Algebra is finite-dimensional, cosemisimple and has commutative bases. It arises as the universal coend with respect to the long canonical functor \omega:C->Vect_k. We show that H is a quotient H=H[G]/I of a Weak Bialgebra H[G] which has a combinatorial description in terms of a finite directed graph G that depends on the choice of a… CONTINUE READING