Generalized Brown representability in homotopy categories

Jiri Rosicky

Brown representability approximates the homotopy category of spectra by means of cohomology functors defined on finite spectra. We will show that if a model category $\cal K$ is suitably determined by $\lambda$-small objects then its homotopy category $Ho(\cal K)$ is approximated by cohomology functors defined on those $\lambda$-small objects. In the case of simplicial sets, we have $\lambda = \omega_1$, i.e., $\lambda$-small means countable.

Keywords: Quillen model category, Brown representability, triangulated category, accessible category

2000 MSC: 18G55, 55P99

Theory and Applications of Categories, Vol. 14, 2005, No. 19, pp 451-479.

Revised 2008-01-30. Original version at

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