Brown representability often fails for homotopy categories of complexes

Details Brown representability often fails for homotopy categories of complexes Brown representability often fails for homotopy categories of complexes

2010-12-18

arxiv.org/abs/1012.4109v2

J. K-Theory 9 (2012) 151-160

Mathematics

Category Theory

9 pages; version 2: minor changes, references added and updated, Remark 11 on the existence of product generators added

Scientific paper

10.1017/is011010026jkt167

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.

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