Baer invariants in semi-abelian categories II: Homology

Everaert, Tomas;Van der Linden, Tim
(2004) Theory and Applications of Categories — Vol. 12, n° 4, p. 195-224 (2004)

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This article treats the problem of deriving the reflector of a semi-abelian category Alpha onto a Birkhoff subcategory Beta of Alpha. Basing ourselves on Carrasco, Cegarra and Grandje´an’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.
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Everaert, T., & Van der Linden, T. (2004). Baer invariants in semi-abelian categories II: Homology. Theory and Applications of Categories, 12(4), 195-224. https://hdl.handle.net/2078.5/61317 (Original work published 2004)