  In [BK], it is shown that the Turaev-Viro invariants defined for a spherical
fusion category $\mathcal{A}$ extends to invariants of 3-manifolds with
corners. In [Kir], an equivalent formulation for the 2-1 part of the theory
(2-manifolds with boundary) is described using the space of "stringnets with
boundary conditions" as the vector spaces associated to 2-manifolds with
boundary. Here we construct a similar theory for the 3-2 part of the 4-3-2
theory in [CY1993].
