Generalized Brown representability in homotopy categories

Details Generalized Brown representability in homotopy categories Generalized Brown representability in homotopy categories

2005-06-09

arxiv.org/abs/math/0506168v3

Theory Appl. Categ. 14 (2005), 451-479

Mathematics

Category Theory

This is the correction of the original submission which was published in Theory Appl. Categ. 14 (2005), 451-479. Propositions

Scientific paper

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 $\Ho(\mathcal K)$.

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