Global spaces and the homotopy theory of stacks

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