  We provide a description of adequate categorical data to give a Turaev-Viro
type state-sum construct of invariants of 3-manifolds with a system of defects,
generalizing the Dijkgraaf-Witten type invariants of our earlier work. We term
the defects in our construction defects-with-structure because algebraic data
associated to them is in general richer than a module category over the
spherical fusion category from which the theory is constructed when no defect
is present.
