Weak fibration categories induce good model structures on Pro-categories.

Pro categories have been introduced by the Grothendieck school to treat arithmetic as a chapter of algebraic geometry. A step further is to consider it as a chapter of algebraic topology (i.e. in the setting of model categories). Isaksen has shown that given a model category C, Pro(C) can be equipped with a model structure. However some categories of interest in "Arithmetic topology" can not be equipped with a "projective" model structure enabling to derive some functors of interest. The aim of this talk is to show that a weaker notion at the level of C ("weak fibration category") induces on Pro(C) a model structure which fulfills all the properties needed for the applications in mind.