The HELP-Lemma And Its Converse In Quillen Model Categories

R. M. Vogt

We show that a map p: X \to Y 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.

Journal of Homotopy and Related Structures, Vol. 6(2011), No. 1, pp. 115-118