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Central extensions in Mal'tsev varieties

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G. Janelidze and G.M. Kelly

We show that every algebraically-central extension in a Mal'tsev variety -
that is, every surjective homomorphism $f : A \longrightarrow B$ whose
kernel-congruence is contained in the centre of $A$, as defined using the
theory of commutators - is also a central extension in the sense of
categorical Galois theory; this was previously known only for varieties of
$\Omega$-groups, while its converse is easily seen to hold for any
congruence-modular variety.

Keywords:

2000 MSC: 08B05, 08C05, 18G50.

*Theory and Applications of Categories*, Vol. 7, 2000, No. 10, pp 219-226.

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