... Fi∨X).This extends to the case where F is unbounded, under the assumptionthat for any X ∈C, then Fr(X) = 0 for |r|0 and for any X∈C, thenFr∨(X) = 0 for |r|0.4.1.5. Assume C and Care ... underextensions and direct summands and containing EiT for all i ≥ 0 and T asimple object of A such that FT = 0. Then, in general, not every projectiveobject of A is in F (cf. the case of S3 and p ... A is a weight vector.Proof. Let M be an object of A with exactly two composition factorsS1 and S2. Assume S1 and S2are in different weight spaces. Then, there areε ∈{± }and {i, j} = {1,...