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

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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},
     publisher = {mathdoc},
     volume = {14},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2005_14_a18/}
}
TY  - JOUR
AU  - Jiri Rosicky
TI  - Generalized Brown representability in homotopy categories
JO  - Theory and applications of categories
PY  - 2005
SP  - 451
EP  - 479
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TAC_2005_14_a18/
LA  - en
ID  - TAC_2005_14_a18
ER  - 
%0 Journal Article
%A Jiri Rosicky
%T Generalized Brown representability in homotopy categories
%J Theory and applications of categories
%D 2005
%P 451-479
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TAC_2005_14_a18/
%G en
%F TAC_2005_14_a18
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/