  Topological domain walls separating 2+1 dimensional topologically ordered
phases can be understood in terms of Witt equivalences between the UMTCs
describing anyons in the bulk topological orders. However, this picture does
not provide a framework for decomposing stacks of multiple domain walls into
superselection sectors - i.e., into fundamental domain wall types that cannot
be mixed by any local operators. Such a decomposition can be understood using
an alternate framework in the case that the topological order is anomaly-free,
in the sense that it can be realized by a commuting projector lattice model. By
placing these Witt equivalences in the context of a 3-category of potentially
anomalous (2+1)D topological orders, we develop a framework for computing the
decomposition of parallel topological domain walls into indecomposable
superselection sectors, extending the previous understanding to topological
orders with non-trivial anomaly. We characterize the superselection sectors in
terms of domain wall particle mobility, which we formalize in terms of
tunnelling operators. The mathematical model for the 3-category of topological
orders is the 3-category of fusion categories enriched over a fixed unitary
modular tensor category.
