# 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.

http://www.tac.mta.ca/tac/volumes/14/19/14-19.dvi
http://www.tac.mta.ca/tac/volumes/14/19/14-19.ps
http://www.tac.mta.ca/tac/volumes/14/19/14-19.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/19/14-19.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/14/19/14-19.ps

Revised 2008-01-30. Original version at
http://www.tac.mta.ca/tac/volumes/14/19/14-19a.dvi

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