Compact inverse categories

Chris Heunen, Robin Cockett

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract / Description of output

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.
Original languageEnglish
Title of host publicationSamson Abramsky on Logic and Structure in Computer Science and Beyond
Publication statusPublished - 4 Aug 2023

Publication series

NameOutstanding Contributions to Logic


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