Montoli, Andrea; Rodelo, Diana; Van Der Linden, Tim

A Galois theory for monoids

Theory Appl. Categ. 29, 198-214, electronic only (2014)


Summary: 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.

Mathematics Subject Classification

20M32, 20M50, 11R32, 19C09, 18F30


categorical Galois theory, homogeneous split epimorphism, special homogeneous surjection, central extension, group completion, Grothendieck group