Cohomologically triangulated categories II

A cohomologically triangulated category is an additive category A together with a translation functor t and a cohomology class del is an element of H(3)(A,t) such that any good translation track category representing del is a triangulated track category. In this paper we give purely cohomological conditions oil del which imply that (A,t,del) is a cohomologically triangulated category, avoiding the use or track categories. This yields a purely cohomological characterization of triangulated cohomology classes.