A Galois theory for monoids

Montoli, Andrea;Ferreira Rodelo, Diana;Van der Linden, Tim
(2014) Theory and Applications of Categories — Vol. 29, n° 7, p. 198-214 (2014)

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  • Montoli, AndreaUCLouvain
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  • Ferreira Rodelo, DianaUCLouvain
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  • Van der Linden, Timorcid-logoUCLouvain
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Abstract
We show that the adjunction between monoids and groups obtained via the Grothendieck group construction is admissible, relatively to surjective homomorphisms, in the sense of categorical Galois theory. The central extensions with respect to this Galois structure turn out to be the so-called special homogeneous surjections.
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Montoli, A., Ferreira Rodelo, D., & Van der Linden, T. (2014). A Galois theory for monoids. Theory and Applications of Categories, 29(7), 198-214. https://hdl.handle.net/2078.5/59902 (Original work published 2014)