Skip to content
DraconiticResearch
Search Sources API
190,851 studies31 sourcesUpdated 58 min ago
PreprintarXiv licencearXiv

Gros Topoi as Partially Lax Limits of Petit Topoi

  • Fabio Neugebauer
  • Qi Zhu
Open at sourcePDFDOICite

Abstract

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

Related

  1. Sequential Certification of Partially Identified Product Targets: Information Limits and Adaptive Sampling
    Abdallah Skiredj, Abderrahman Skiredj, Amal El Fallah Seghrouchni
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  2. C'est un petit val qui mousse de fonctions
    Alexis Marin Bozonat, Greg Mcshane
    HALPreprintCC BY 4.0Full textGeneral mathematicsHAL
  3. A parametrization of nonassociative Petit algebras K[t;σ]/K[t:σ](tm−a) up to equivalence
    Monica Nevins, Susanne Pumpluen
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. SCATTERING OF WATER WAVES IN PRESENCE OF A PARTIALLY IMMERSED OBSTACLE
    Debayan Maity, Vicente Ocqueteau, Marius Tucsnak
    HALPreprintPublisher termsFull textGeneral mathematicsHAL
  5. Debiasing ML- or AI-Generated Regressors in Partially Linear Models
    Jingwen Zhang, Wendao Xue, Yifan Yu +1
    Information Systems ResearchPeer-reviewedLicence not stated9 citedStatisticsOpenAlex

Cite

BibTeXRIS
BibTeX
@misc{neugebauer2026gros,
  title = {{Gros Topoi as Partially Lax Limits of Petit Topoi}},
  author = {Fabio Neugebauer and Qi Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35119},
  eprint = {2609.35119},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35119},
}
RIS
TY  - UNPB
TI  - Gros Topoi as Partially Lax Limits of Petit Topoi
AU  - Fabio Neugebauer
AU  - Qi Zhu
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35119
UR  - https://arxiv.org/abs/2609.35119
AB  - We prove that the sheaf ∞-topos associated to a geometric site in the sense of Lurie can be written as a partially lax limit of smaller sheaf ∞-topoi. This is thus a formalization of Lurie's vision for fractured ∞-topoi to axiomatize the relation between gros and petit topoi. As a consequence, we realize the ∞-topos of κ-small condensed anima as a partially lax limit of sheaf ∞-topoi over extremally disconnected spaces, marked at the open embeddings. Moreover, we deduce a gros version of the étale exodromy theorem.
ER  -