ScalingStacks

Corollary 9.24 (of proposition 9.21). There is a functor

$$\mathrm{Loc}:{\mathcal{M}}_{\mathrm{loc}}^{\kappa}\longrightarrow\underline{{\mathcal{M}}_{\mathrm{wloc}}^{\kappa}}$$

such that $\mathrm{Loc}({\mathcal{U}}_{\mathrm{loc}}^{\kappa}({\mathcal{A}}))\simeq V({\mathcal{A}})$, for every small stable $\infty$-category ${\mathcal{A}}$.