Baer invariants in semi-abelian categories II: Homology

T. Everaert and T. Van der Linden

This article treats the problem of deriving the reflector of a semi-abelian category $\cal A$ onto a Birkhoff subcategory $\cal B$ of $\cal A$. Basing ourselves on Carrasco, Cegarra and Grandjean's homology theory for crossed modules, we establish a connection between our theory of Baer invariants with a generalization---to semi-abelian categories---of Barr and Beck's cotriple homology theory. This results in a semi-abelian version of Hopf's formula and the Stallings-Stammbach sequence from group homology.

Keywords: Baer invariant, semi-abelian category, cotriple homology

2000 MSC: Primary 20J05 18G50 18C15; Secondary 18G30 18G35 18E25

Theory and Applications of Categories, Vol. 12, 2004, No. 4, pp 195-224.

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