Generalized Brown representability in homotopy categories

J. Rosicky

Generalized Brown representability in homotopy categories

Category Theory 2009-12-03 v3

Authors: J. Rosicky

Abstract

We show that the homotopy category of a combinatorial stable model category $\ck$ is well generated. It means that each object $K$ of $\Ho(\ck)$ is an iterated weak colimit of $\lambda$ -compact objects for some cardinal $\lambda$ . A natural question is whether each $K$ is a weak colimit of $\lambda$ -compact objects. We show that this is related to (generalized) Brown representability of $\Ho(\mathcal K)$ .

Keywords

homotopy theory stable categories algebraic k-theory

Cite

@article{arxiv.math/0506168,
  title  = {Generalized Brown representability in homotopy categories},
  author = {J. Rosicky},
  journal= {arXiv preprint arXiv:math/0506168},
  year   = {2009}
}

Comments

This is the correction of the original submission which was published in Theory Appl. Categ. 14 (2005), 451-479. Propositions 4.2 and 4.3 from the original submission are not correct. Thus the claims of Theorems 5.4, 5.7 and their Corollaries 5.8, 5.9 and 5.10 remain open. I am grateful to J. F. Jardine and F. Muro for pointing it out

Generalized Brown representability in homotopy categories

Abstract

Keywords

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