# 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} }

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

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