We study Quillen's model category structure for homotopy of simplicialobjects in the context of Janelidze, Marki and Tholen's semi-abeliancategories. This model structure exists as soon as the base category A isregular Mal'tsev and has enough regular projectives; then the fibrations arethe Kan fibrations of simplicial objects in A. When, moreover, A issemi-abelian, weak equivalences and homology isomorphisms coincide.
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