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. ). 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.