English

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.

Keywords

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

R2 v1 2026-07-22T17:38:26.140Z