A Galois theory of monoids

Van der Linden, Tim
(2014) Categorical Methods in Algebra and Topology — Location: Coimbra, Portugal (23.January.2014)

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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. As a consequence, special homogeneous surjections are reflective amongst surjective monoid morphisms.
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Van der Linden, T. (2014). A Galois theory of monoids. Categorical Methods in Algebra and Topology, Coimbra, Portugal. https://hdl.handle.net/2078.5/268295