Commutators and central extensions in universal algebra (Q1855451)

Any congruence-modular variety \(V\) is equipped with a good theory of commutators. This makes it possible to define abelian objects and central extensions in \(V\). These concepts are classical for the variety of groups. The paper proves that central extensions defined in this way coincide with the categorical central extensions [cf. \textit{G. Janelidze} and \textit{G. M. Kelly}, ``Central extensions in universal algebra: A unification of three notions'', Algebra Univers. 44, 123-128 (2000; Zbl 1013.08009)] with respect to the full subcategory of abelian objects. The author uses the categorical approach to the theory of commutators suggested by \textit{G. Janelidze} and \textit{M. C. Pedicchio} [``Pseudogroupoids and commutators'', Theory Appl. Categ. 8, 408-456 (2001; Zbl 1008.18006)].