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arXiv · 2407.06877

Global spaces and the homotopy theory of stacks

Adrian Clough·Bastiaan Cnossen·Sil Linskens
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Abstract

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.

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Adrian Clough, Bastiaan Cnossen, Sil Linskens. 2024-07-09. Global spaces and the homotopy theory of stacks. https://arxiv.org/abs/2407.06877

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