2010/12/31 by George Ciprian Modoi, Jan Šťovíček, Jan Stovicek
Mathematics · #Abelian group #Algebraic structures and combinatorial models #Dual (grammatical number) #Geometric and Algebraic Topology #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy category #Homotopy lifting property #Subcategory #math.AT #math.CT #msc:16D90 #msc:18G35 #msc:55U35
paper · pdf · doi:10.1017/is011010026jkt167
published as J. K-Theory 9 (2012) 151-160 · 9 pages; version 2: minor changes, references added and updated, Remark 11 on the existence of product generators added
arxiv created 2011/08/19 · openalex publication_date 2011/11/07 · arxiv updated 2012/02/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract We show that for the homotopy category K (Ab) of complexes of abelian groups, both Brown representability and Brown representability for the dual fail. We also provide an example of a localizing subcategory of K (Ab) for which the inclusion into K (Ab) does not have a right adjoint.