2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164751We 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.5 pagesCategory TheoryAlgebraic Topology18E30; 55U35text