We construct higher categories of iterated spans, possibly equipped with
extra structure in the form of "local systems", and classify their fully
dualizable objects. By the Cobordism Hypothesis, these give rise to framed
topological quantum field theories, which are the framed versions of the
"classical" TQFTs considered in the quantization programme of
Freed-Hopkins-Lurie-Teleman.
Using this machinery, we also construct an infinity-category of Lagrangian
correspondences between symplectic derived algebraic stacks and show that all
its objects are fully dualizable.Comment: Accepted version, plus corrections to Remarks 10.5 and 10.7. 64 page
