ABSTRACT

Let ℌ be a connected hereditary abelian category with finite dimensional homomorphism and extension spaces. If ℌ contains a tilting object then ℌ has almost split sequences and if ℌ is not a module category this yields an equivalence τ. We consider here τ-invariant additive functions on ℌ and show as a main result that ℌ contains simple objects iff there exists a nonnegative additive τ–invariant function.