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