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.

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2011 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.