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.
Keywords: categorical Galois theory; homogeneous split epimorphism; special homogeneous surjection; central extension; group completion; Grothendieck group
2010 MSC: 20M32, 20M50, 11R32, 19C09, 18F30
Theory and Applications of Categories, Vol. 29, 2014, No. 7, pp 198-214.