Simplicial homotopy in semi-abelian categories

摘要

We study Quillen's model category structure for homotopy of simplicial ob-jects in the context of Janelidze, Marki and Tholen's semi-abelian categories.This model structure exists as soon as A is regular Mal'tsev and has enoughregular projectives; then the fibrations are the Kan fibrations of SA. When,moreover, A is semi-abelian, weak equivalences and homology isomorphismscoincide.