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Hi,

let's start with a left exact functor $F: A\longrightarrow B$ of abelian categories, where the derived functor $RF: D^{+}(A)\longrightarrow D^{+}(B)$ exists. Furthermore the class of F-acyclic objects be adapted to F and furthermore F of finite cohomological dimension.

My question: how can I find a natural number n with the following property: if

$X_n\rightarrow X_{n-1}\rightarrow ...\rightarrow X_{o}$ is exact in $A$ with $X_n,...,X_1$ F-acyclic, then also $X_{o}$ is F-acyclic.

Regards!

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5 
 Crossposted to math.SE: math.stackexchange.com/q/56015 Please don't post the same question on two different platforms. This leads to duplication of efforts and makes the contributors less willing to answer your question: you already posted your last question here: mathoverflow.net/q/72196 and on math.SE: math.stackexchange.com/q/55860 Decide to post on one forum and wait a little longer than three hours (maybe a few days...) before posting on the other. If you crosspost then it would be a matter of courtesy to point that out. – Theo Buehler Aug 6 2011 at 23:48
3 
 Dear Descartes: I've just answered the question on math.SE, but am voting to close here, because the result you have asked about is a standard exercise in homological algebra. – Akhil Mathew Aug 6 2011 at 23:58

closed as off topic by Akhil Mathew, Qiaochu Yuan, Gjergji Zaimi, Ryan Budney, Tom Leinster Aug 7 2011 at 0:21

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