18 LEONID POSITSELSKI

the respective directions, the condition that C[−1] ⊂ C can be dropped. Moreover,

the subcategories D 0 and D 1 described in this remark have a semiorthogonality

property, HomD(Y, Z) = 0 for all Y ∈ D 1 and Z ∈ D 0 (cf. [45]). Indeed, given

an object Z in a triangulated category D, the class of all objects Y ∈ D such that

HomD(Y, Z) = 0 is closed under infinite direct sums and countably iterated exten-

sions, as one can see using the fact that the first derived functor of projective limit

of a sequence of surjective maps of abelian groups vanishes.