The HELP-Lemma and its converse in Quillen model categories

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.

arXiv comment5 pages

Cited by in corpus (4)

• On the homotopy theory of enriched categories
• Weak model categories in classical and constructive mathematics
• Homotopy homomorphisms and the classifying space functor
• Quasicategories of Frames of Cofibration Categories