Geodesic
Generalized Brown representability in homotopy categories
Theory and applications of categories, Tome 14 (2005), pp. 451-479
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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.

Classification : 18G55, 55P99
Keywords: Quillen model category, Brown representability, triangulated category, accessible category 
@article{TAC_2005_14_a18,
     author = {Jiri Rosicky},
     title = {Generalized {Brown} representability in homotopy categories},
     journal = {Theory and applications of categories},
     pages = {451--479},
     year = {2005},
     volume = {14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2005_14_a18/}
}
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Jiri Rosicky. Generalized Brown representability in homotopy categories. Theory and applications of categories, Tome 14 (2005), pp. 451-479. http://geodesic.mathdoc.fr/item/TAC_2005_14_a18/