Geodesic
A Galois theory for monoids
Theory and applications of categories, Tome 29 (2014), pp. 198-214

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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.

Publié le :
Classification : 20M32, 20M50, 11R32, 19C09, 18F30
Keywords: categorical Galois theory, homogeneous split epimorphism, special homogeneous surjection, central extension, group completion, Grothendieck group 
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     author = {Andrea Montoli and Diana Rodelo and Tim Van der Linden},
     title = {A {Galois} theory for monoids},
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     pages = {198--214},
     publisher = {mathdoc},
     volume = {29},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a6/}
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Andrea Montoli; Diana Rodelo; Tim Van der Linden. A Galois theory for monoids. Theory and applications of categories, Tome 29 (2014), pp. 198-214. http://geodesic.mathdoc.fr/item/TAC_2014_29_a6/