Brown representability often fails for homotopy categories of complexes
Category Theory
2012-02-17 v2 Algebraic Topology
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.
Cite
@article{arxiv.1012.4109,
title = {Brown representability often fails for homotopy categories of complexes},
author = {George Ciprian Modoi and Jan Stovicek},
journal= {arXiv preprint arXiv:1012.4109},
year = {2012}
}
Comments
9 pages; version 2: minor changes, references added and updated, Remark 11 on the existence of product generators added