T. Van der Linden, Simplicial homotopy in semi-abelian categories, J. K-Theory 4 (2009), no. 2, 379-390.Additional comments (with thanks to George Peschke)
The homology part of Lemma 3.4 is (clearly!) only valid for indexes n bigger than 0. As a consequence, the induction in the proof of Proposition 3.9 does not get off the ground. Nevertheless, the result is correct. Julia Goedecke fixes the proof with Theorem 3.9 in her articleJ. Goedecke, Homology in relative semi-abelian categories, Appl. Categ. Structures 21 (2012) No. 6, 523-543.In this paper the context is also enlarged to a relative setting. My Proposition 3.9 is the special case of her Theorem 3.9 where the class E consists of all regular epimorphisms and A-1 is zero.
An alternative, more homotopical, approach to the key Theorem 5.6 is given in forthcoming joint work with George Peschke.
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