Brown representability often fails for homotopy categories of complexes

Published 18 Dec 2010 in math.CT and math.AT | (1012.4109v2)

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.

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