Global spaces and the homotopy theory of stacks

We show that the ∞-category of global spaces is equivalent to the homotopy localization of the ∞-category of sheaves on the site of separated differentiable stacks, following a philosophy proposed by Gepner-Henriques. We further prove that this ∞-category of sheaves is a cohesive ∞-topos and that it fully faithfully contains the singular-cohesive ∞-topos of Sati-Schreiber.