Simplicial homotopy in semi-abelian categories

Published as
T. Van der Linden, Simplicial homotopy in semi-abelian categories, J. K-Theory 4 (2009), no. 2, 379-390.
Preprint arXiv:math/0607076
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 article
J. Goedecke, Homology in relative semi-abelian categories, Appl. Categ. Structures 21 (2012) No. 6, 523-543.
Preprint pdf
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.

Back to Tim Van der Linden's website