Closed model category structures on the category of chain functors

In the category Ch of chain functors one can introduce fibrations (Section 3), cofibrations and weak equivalences (Section 4), satisfying all the properties of a closed model category as defined by D. Quillen except for the existence of finite limits and colimits. Nevertheless we show that there exists a canonically defined suspension—as well as a loop functor, which are invertible, turning the homotopy category Chh into a stable category (Section 8).