Shifted geometric quantization

Understand

We introduce geometric quantization in the setting of shifted symplectic structures.

• We define Lagrangian fibrations and prequantizations of shifted symplectic stacks and their geometric quantization.
• In addition, we study many examples including symplectic groupoids, Hamiltonian spaces and moduli spaces of flat connections.
• In the case of Hamiltonian spaces we prove a derived analog of the "quantization commutes with reduction" principle.