In this chapter, we show that under rather mild hypothesis, the center of a rigid category is the category of modules over a quasitriangular Hopf monad. This allows us to compute the coend of the center of a pivotal fusion category. As an application, we prove Theorems 5.3–5.5. This chapter is based on [BV2, BV3].
Turaev, V., & Virelizier, A. (2017). Monadicity of the center. In Progress in Mathematics (Vol. 322, pp. 191–225). Springer Basel. https://doi.org/10.1007/978-3-319-49834-8_9