The HELP-Lemma and its converse in Quillen model categories

R. M. Vogt

The HELP-Lemma and its converse in Quillen model categories

Algebraic Topology 2015-03-17 v1

Authors: R. M. Vogt

Abstract

We show that a map between fibrant objects in a closed model category is a weak equivalence if and only if it has the right homotopy extension lifting property with respect to all cofibrations. The dual statement holds for maps between cofibrant objects.

Keywords

HELP lemma Quillen model category weak equivalence fibrant object cofibrant object right homotopy extension lifting property

Cite

@article{arxiv.1004.5249,
  title  = {The HELP-Lemma and its converse in Quillen model categories},
  author = {R. M. Vogt},
  journal= {arXiv preprint arXiv:1004.5249},
  year   = {2015}
}