On satellites in semi-abelian categories: Homology without projectives

Julia Goedecke and Tim Van der Linden, On satellites in semi-abelian categories: Homology without projectives, Math. Proc. Cambridge Philos. Soc. 147 (2009), no. 3, 629-657.
Final pdf (copyright Cambridge Philosophical Society).

Theorem 5.6 is not true as it stands, because $\mathsf{End} p$ is not initial in $\widehat{\mathsf{End}}p$. Indeed, the very last sentence of the proof is wrong: the zero map $p\rightarrow !_P$ is not a composition as claimed, and is in fact not connected to those compositions.

However, Proposition 5.5 is still correct and can be used instead of Theorem 5.6 in the subsequent examples and comments.

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