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.
A Galois theory for monoids : dedicated to Manuela Sobral on the occasion of her seventieth birthday / A. Montoli, D. Rodelo, T. Van Der Linden. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 29:(2014), pp. 198-214.
A Galois theory for monoids : dedicated to Manuela Sobral on the occasion of her seventieth birthday
A. MontoliPrimo
;
2014
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.
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