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arXiv · 2011.03027

Higher sheaf theory I: Correspondences

Germán Stefanich
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Abstract

We prove a universal property for the $(\infty, n)$-category of correspondences, generalizing and providing a new proof for the case $n = 2$ from [GR17]. We also provide conditions under which a functor out of a higher category of correspondences of $\mathcal{C}$ can be extended to a higher category of correspondences of the free cocompletion of $\mathcal{C}$. These results will be used in the sequels to this paper to construct $(\infty, n)$-categorical versions of the theories of quasicoherent and ind-coherent sheaves in derived algebraic geometry.

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Germán Stefanich. 2020-11-05. Higher sheaf theory I: Correspondences. https://arxiv.org/abs/2011.03027

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