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Simplicial homotopy in semi-abelian categories

Tim Van der Linden
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Abstract

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

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Tim Van der Linden. 2006-07-04. Simplicial homotopy in semi-abelian categories. https://doi.org/10.1017/is008008022jkt070

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