A Boundary Characterization of Turaev-Viro TQFTs

We consider three-dimensional topological field theories on manifolds with boundary defects and identify explicit boundary locality conditions. We show that these conditions imply a state sum construction of the given TQFT. As a consistency check, we prove that Turaev-Viro state sum models obey the boundary locality conditions. Recent progress [Faria Martins J., Meusburger C., Adv. Math. 494 (2026), 110923, 102 pages, arXiv:2410.18049] in the description of defects in Dijkgraaf-Witten theories enables us to show that these theories likewise satisfy boundary locality. This directly implies that Dijkgraaf-Witten TQFTs with boundary defects admit a state sum description.