English

On coherent topoi & coherent $1$-localic $\infty$-topoi

Algebraic Geometry 2019-07-12 v2 Algebraic Topology Category Theory

Abstract

In this note we prove the following useful fact that seems to be missing from the literature: the \infty-category of coherent ordinary topoi (in the sense of SGA4) is equivalent to the \infty-category of coherent 11-localic \infty-topoi (in Lurie's sense). We also collect a number of examples of coherent geometric morphisms between \infty-topoi coming from algebraic geometry.

Keywords

Cite

@article{arxiv.1904.01877,
  title  = {On coherent topoi & coherent $1$-localic $\infty$-topoi},
  author = {Peter J. Haine},
  journal= {arXiv preprint arXiv:1904.01877},
  year   = {2019}
}

Comments

Comments very welcome. v2: 13 pages. Corrected some omissions and typos in v1 and clarified a few points. arXiv admin note: substantial text overlap with arXiv:1807.03281

R2 v1 2026-06-23T08:27:51.971Z