We recall that three-dimensional topological field theories with boundaries
form a natural geometric realization for two-dimensional tensor network
models. The entries of various tensors (PEPS, MPO) arise in the state-sum
construction as evaluations of tetrahedral graphs on spheres. They are thus (mixed) 6j-symbols.
We extend these evaluations of graphs on spheres to include general configurations
of surface defects and bulk Wilson lines. This leads to
an intrinsically three-dimensional calculus, yielding
tensors that still can be computed in terms of traces.