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The HELP-Lemma and its converse in Quillen model categories

2010/04/29 by R. M. Vogt, Vogt, R. M. · 1 citation
Mathematics · #55P05 #55P10 #55P30 #55U35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P05 #msc:55P10 #msc:55P30 #msc:55U35

paper · pdf · doi:10.48550/arxiv.1004.5249

5 pages

arxiv created 2010/04/29 · openalex publication_date 2010/04/29 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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