Quantum Betti geometric Langlands functor

Abstract: We construct the quantum geometric Langlands functor in the Betti setting via Whittaker coefficients. We show that the functor is compatible with the 2-Fourier-Mukai equivalence between sheaves of categories over 2-stacks $\operatorname{Ge}{Z_G}$ and $\operatorname{Ge}{π_1(\check{G})}$, which classify gerbes on $X$ with respect to the center $Z_G$ of $G$ and algebraic fundamental group $π_1(\check{G})$ of $\check{G}$.