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arXiv · 2609.35119

Gros Topoi as Partially Lax Limits of Petit Topoi

Fabio Neugebauer·Qi Zhu
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Abstract

We prove that the sheaf $\infty$-topos associated to a geometric site in the sense of Lurie can be written as a partially lax limit of smaller sheaf $\infty$-topoi. This is thus a formalization of Lurie's vision for fractured $\infty$-topoi to axiomatize the relation between gros and petit topoi. As a consequence, we realize the $\infty$-topos of $κ$-small condensed anima as a partially lax limit of sheaf $\infty$-topoi over extremally disconnected spaces, marked at the open embeddings. Moreover, we deduce a gros version of the étale exodromy theorem.

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BibTeXRIS

Fabio Neugebauer, Qi Zhu. 2026-09-28. Gros Topoi as Partially Lax Limits of Petit Topoi. https://arxiv.org/abs/2609.35119

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