Galois theory and commutators
We explain how the relative commutator with respect to a
subvariety of a variety of omega-groups can be described in terms of
categorical Galois theory. This extends the known correspondence between
Fröhlich's and Janelidze and Kelly's notions of central extension.
Basing ourselves on the concept of double central extension, thus we
obtain a commutator which is defined relative to a Birkhoff subcategory
B of a semi-abelian category A. In case the subcategory B is determined
by the abelian objects in A we regain Huq's commutator.
Tim Van der Linden (CMUC/FCT)
December 02, 2008