Simplicial homotopy in semi-abelian categories
K-Theory and Homology
2010-06-10 v1
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.
Cite
@article{arxiv.math/0607076,
title = {Simplicial homotopy in semi-abelian categories},
author = {Tim Van der Linden},
journal= {arXiv preprint arXiv:math/0607076},
year = {2010}
}
Comments
12 pages