Compact inverse categories

Robin Cockett; Chris Heunen

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arXiv · 1906.04248

Compact inverse categories

Robin Cockett·Chris Heunen

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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.

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BibTeX RIS

Robin Cockett, Chris Heunen. 2019-06-10. Compact inverse categories. https://arxiv.org/abs/1906.04248

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