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 -category of coherent ordinary topoi (in the sense of SGA4) is equivalent to the -category of coherent -localic -topoi (in Lurie's sense). We also collect a number of examples of coherent geometric morphisms between -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