A Galois theory for monoids
(2014) 95th Peripatetic Seminar on Sheaves and Logic — Location: Brno, Tchéquie (26.April.2014)
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- A Galois theory for monoids 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 [3]. The central extensions with respect to this Galois structure turn out to be the so-called special homogeneous surjections [1, 2]. This is joint work with Andrea Montoli and Diana Rodelo. References [1] D. Bourn, N. Martins-Ferreira, A. Montoli, and M. Sobral, Schreier split epimorphisms between monoids, Semigroup Forum, in press, 2014. [2] D. Bourn, N. Martins-Ferreira, A. Montoli, and M. Sobral, Schreier split epimorphisms in monoids and in semirings, Textos de Matemática (Série B), vol. 45, Departamento de Matemática da Universidade de Coimbra, 2014. [3] G. Janelidze, Pure Galois theory in categories, J. Algebra 132 (1990), no. 2, 270– 286. [4] A. Montoli, D. Rodelo, and T. Van der Linden, A Galois theory for monoids, Pré-Publicações DMUC 14-06 (2014), 1–19.
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Van der Linden, T. (2014). A Galois theory for monoids. 95th Peripatetic Seminar on Sheaves and Logic, Brno, Tchéquie. https://hdl.handle.net/2078.5/63265