$\Gamma$-geometric correspondence conjecture for quantized fields

Let $X_\Gamma$ be a derived $\Gamma$-space, let $\mathcal D_{\mathrm{coh}}(X_\Gamma)$ be its coherent derived category, and let $\mathsf{Phys}_\Gamma$ be the category of $\Gamma$-physical objects. $\Gamma$-geometric correspondence conjecture. There exists a functor

$$\mathfrak Q_\Gamma:\mathcal D_{\mathrm{coh}}(X_\Gamma)\to\mathsf{Phys}_\Gamma$$

assigning to each derived $\Gamma$-object its quantized field. This proposes a functorial bridge from coherent derived $\Gamma$-geometry to physical fields; the source supplies no resolution or construction establishing it.