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Higher sheaf theory I: Correspondences

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arxiv 2011.03027 v1 pith:LXGUVCN5 submitted 2020-11-05 math.AT math.AGmath.CT

Germán Stefanich This is my paper · ORCID
classification math.ATmath.AGmath.CT
keywords correspondencescategoryhigherinftymathcalalgebraiccasecategorical
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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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  1. Enriched $\infty$-categories as marked module categories

    math.AT 2025-01 conditional novelty 8.0 of 10

    Enriched ∞-categories are equivalent to presentable module categories marked by an atomically generating family of representables.

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