A Galois theory for monoids

Andrea Montoli, Diana Rodelo and Tim Van der Linden

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.

Published 2014-05-01.


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