I would like to ask if the following statement can be true: bosonic topological orders in $n$-dimensional space-time 1-to-1 correspond to unitary fully dualizable fully extended TQFT in $n$-dimensions.
Bosonic topological order has been defined in physics using generalized local unitary equivalence in arXiv:1406.5090 Roughly, it corresponds to unitary TQFT, with boundaries, and the boundaries can have boundaries, etc.