Tensor network states provide a comprehensive framework for the analytic and numerical study of strongly correlated many-body systems. In recent years, this framework has been successfully applied to topological phases of matter. In this talk, I will present two dual tensor network representations of the $(3+1)d$ toric code ground state subspace, which are obtained by initially imposing either family of stabilizer constraints. I will discuss topological properties of the model from the point of view of these virtual symmetries, demonstrate that one of these representations is stable to all local tensor perturbations — including those that do not map to local operators on the physical Hilbert space — and explain, both from a physical and category theoretical viewpoint, how the distinguishing properties of these representations are related to the phenomenon of bulk-boundary correspondence.