English

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

R2 v1 2026-06-21T17:01:02.889Z