@inbook{a041da95cbff4aca9d46d91178cfda78,
title = "Compact inverse categories",
abstract = "The Ehresmann-Schein-Nambooripad theorem gives a structure theorem for inverse monoids: they are inductive groupoids. A particularly nice case due to Jarek is that commutative inverse monoids become semilattices of abelian groups. It has also been categorified by DeWolf-Pronk to a structure theorem for inverse categories as locally complete inductive groupoids. We show that in the case of compact inverse categories, this takes the particularly nice form of a semilattice of compact groupoids. Moreover, one-object compact inverse categories are exactly commutative inverse monoids. Compact groupoids, in turn, are determined in particularly simple terms of 3-cocycles by Baez-Lauda. ",
author = "Chris Heunen and Robin Cockett",
note = "Funding Information: Date: January 13, 2023. Supported by EPSRC Fellowship EP/R044759/1. We thank Peter Hines for pointing out that the proof of Proposition 9 could be simplified, Martti Karvonen for the idea of the proof of Lemma 23, and Phil Scott for pointing out Theorem 5. Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2023",
month = aug,
day = "4",
doi = "10.1007/978-3-031-24117-8_22",
language = "English",
volume = "25",
series = "Outstanding Contributions to Logic",
publisher = "Springer",
pages = "813--832",
booktitle = "Samson Abramsky on Logic and Structure in Computer Science and Beyond",
address = "United Kingdom",
}