Cohomologically triangulated categories II

Abstract

AbstractA cohomologically triangulated category is an additive categoryAtogether with a translation functortand a cohomology class Δ ∈H3(A,t) such that any good translation track category representing Δ is a triangulated track category. In this paper we give purely cohomological conditions on Δ which imply that (A,t,Δ) is a cohomologically triangulated category, avoiding the use of track categories. This yields a purely cohomological characterization of triangulated cohomology classes.