In this chapter, we associate with each pivotal K -category a family of modules called multiplicity modules. Then we introduce an invariant of colored graphs which takes values in tensor products of multiplicity modules. This invariant will be our main tool in the construction of a 3-dimensional TQFT in the next chapter.
Turaev, V., & Virelizier, A. (2017). Multiplicity modules and colored graphs. In Progress in Mathematics (Vol. 322, pp. 257–272). Springer Basel. https://doi.org/10.1007/978-3-319-49834-8_12