We derive from a spherical fusion category with invertible dimension a graph TQFT which applies to colored ribbon graphs in 3-dimensional cobordisms. For cobordisms with empty graphs, we recover the TQFT of Chapter 13.
Turaev, V., & Virelizier, A. (2017). The state sum graph TQFT. In Progress in Mathematics (Vol. 322, pp. 321–398). Springer Basel. https://doi.org/10.1007/978-3-319-49834-8_15