Gapped Boundary Theories in Three Dimensions

We prove a theorem in 3-dimensional topological field theory: Reshetikhin–Turaev theory admits nonzero boundary iff it is Turaev–Viro theory. The proof immediately implies characterization of fusion categories terms dualizability. Our results rely on (special case of) the cobordism hypothesis with singularities. main applies to physics, where an obstruction gapped quantum system admitting Appendices bordism multicategories, 2-dualizable categories, and internal duals may be independent interest.