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.
http://www.tac.mta.ca/tac/volumes/12/4/12-04.dvi
http://www.tac.mta.ca/tac/volumes/12/4/12-04.ps
http://www.tac.mta.ca/tac/volumes/12/4/12-04.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/4/12-04.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/12/4/12-04.ps