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Brown representability often fails for homotopy categories of complexes

Published online by Cambridge University Press:  07 November 2011

George Ciprian Modoi  and
Jan Šťovíček
George Ciprian Modoi
Affiliation:
Babeş–Bolyai University, Faculty of Mathematics and Computer Science, 1, Mihail Kogălniceanu, 400084 Cluj–Napoca, Romaniacmodoi@math.ubbcluj.ro
Jan Šťovíček
Affiliation:
Charles University in Prague, Faculty of Mathematics and Physics, Department of Algebra, Sokolovska 83, 186 75 Praha 8, Czech Republicstovicek@karlin.mff.cuni.cz
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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.

Keywords

Brown representabilityAdjoint functorTriangulated categoryHomotopy category of complexes
Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 1 , February 2012 , pp. 151 - 160
Copyright
Copyright © ISOPP 2011

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