全局空间和堆栈同调理论

arXiv - MATH - Algebraic Topology Pub Date : 2024-07-09 DOI:arxiv-2407.06877

Adrian Clough, Bastiaan Cnossen, Sil Linskens

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摘要

我们证明了全局空间的$\infty$类别等价于在分离可微堆栈上的翮（sheaves）的$\infty$类别的同调局部化，这遵循了Gepner-Henriques提出的哲学。我们进一步证明了这个$\infty$-卷范畴是一个内聚的$\infty$-拓扑，并且它完全忠实地包含了萨蒂-施赖伯的singular-内聚的$\infty$-拓扑。

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Global spaces and the homotopy theory of stacks

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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arXiv - MATH - Algebraic Topology

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