@article{9f6d7d0760e6413ab00ef45817a0e64c,
title = "Decomposition-space slices are toposes",
abstract = "We show that the category of decomposition spaces and CULF maps is locally a topos. Precisely, the slice category over any decomposition space D is a presheaf topos, namely Decomp/D ≃ Psh(tw D).",
author = "Joachim Kock and Spivak, {David I.}",
note = "Funding Information: Received by the editors July 27, 2018, and, in revised form, August 13, 2019. 2010 Mathematics Subject Classification. Primary 18B25, 18G30, 55U10. The first author was supported by grant MTM2016-80439-P (AEI/FEDER, UE) of Spain and grant 2017-SGR-1725 of Catalonia. The second author was supported by AFOSR grants FA9550–14–1–0031 and FA9550–17–1– 0058. Publisher Copyright: {\textcopyright} 2020 American Mathematical Society",
year = "2020",
doi = "10.1090/proc/14834",
language = "English",
volume = "148",
pages = "2317--2329",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "6",
}