Domain Walls in Topological Phases and the Brauer–Picard Ring for Vec (Z/ pZ)

We show how to calculate the relative tensor product of bimodule categories (not necessarily invertible) using ladder string diagrams. As an illustrative example, we compute the Brauer–Picard ring for the fusion category Vec(Z/ pZ) . Moreover, we provide a physical interpretation of all indecomposable bimodule categories in terms of domain walls in the associated topological phase. We show how this interpretation can be used to compute the Brauer–Picard ring from a physical perspective.