Images directes cohomologiques dans les catégories de modèles

Denis-Charles Cisinski

AMS Classification numbers 55U3, 55U40

Institut de Mathématiques de Jussieu
Université Paris 7
Case 7012
2 place Jussieu
75251 Paris cedex 05 France

E-mail: cisinski@math.jussieu.fr

Abstract
Show that every complete model category M
admits homotopy limits, and more generaly
that every functor between small categories
has a cohomological direct image in M (that is
a homotopy right Kan extension). Furthermore,
we study the local behavor of such constructions.
For this purpose, we introduce Grothendieck's
notion of derivator. Derivators correspond to the
intuition of ``a homotopy complete category''
without speaking about models. Forthcoming
papers will show that this setting is rich
enough to define classical homotopy theory
by a simple universal property.