  We call product generator of an additive category a fixed object satisfying
the property that every other object is a direct factor of a product of copies
of it. In this paper we start with an additive category with products and
images, e.g. a module category, and we are concerned with the homotopy category
of complexes with entries in that additive category. We prove that Brown
representability theorem is valid for the dual of the homotopy category if and
only if the initial additive category has a product generator.
