Tim Van der Linden; Tomas Everaert;
Galois theory and commutators
We prove that the relative commutator with respect to a subvariety of a variety of W-groups can be described in terms of categorical Galois theory. This extends the known correspondence between Frohlich's and Janelidze and Kelly's
notions of central extension. As an example we study the reflection of the category of loops to the category of groups where we obtain an interpretation of the associator as a relative commutator.
Pré-publicações do Departamento de Matemática da Universidade de Coimbra