Generalized Brown representability in homotopy categories

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 $\Ho(\mathcal K)$.

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

References in corpus (1)

• Quillen model structures for relative homological algebra

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