The Stacks project

Lemma 64.6.2. An object $E$ of $D(\mathcal{A})$ is contained in $D^+(\mathcal{A})$ if and only if $H^ i(E) =0 $ for all $i \ll 0$. Similar statements hold for $D^-$ and $D^+$.

Proof. Hint: use truncation functors. See Derived Categories, Lemma 13.11.5. $\square$

Comments (2)

Comment #2168 by Alex on

I think this was probably meant to link to Lemma 13.11.5 05RV rather than 13.11.6

Comment #2197 by on

OK, you are right. But of course the discussion in this section is lacking and one has to read a lot more about triangulated categories to correctly parse these statements... Fixed here.

There are also:

  • 5 comment(s) on Section 64.6: Derived categories

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View Lemma 64.6.2 as pdf