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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.
Clough et al. (Tue,) studied this question.