2008/07/11 by Carles Casacuberta, Casacuberta, Carles, Amnon Neeman +1
Mathematics · #18E30 #55U35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CT #msc:18E30 #msc:55U35
paper · pdf · doi:10.48550/arxiv.0807.1872
5 pages
arxiv created 2008/07/11 · openalex publication_date 2008/07/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We exhibit a triangulated category T having both products and coproducts, and a triangulated subcategory S of T which is both localizing and colocalizing, for which neither a Bousfield localization nor a colocalization exists. It follows that neither the category S nor its dual satisfy Brown representability. Our example involves an abelian category whose derived category does not have small Hom-sets.