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I'm not sure how I can show the following:

If F is a left exact functor from an abelian category A to an abelian category B, whose derived functor RF in the sense of derived categories exists, then the following holds:

if $Z^{.}$ is a complex consisting of F-acyclic objects in A, then $RF(Z^{.})$ is equal to $KF(Z^{.})$; with the last symbol I just mean: apply F to the complex $Z^{.}$ and understand the result as belonging to $D^{+}(B)$.

I don't want to assume the existence of F-adapted classes or enough Injectives, just the Existence of RF.

Thanks a lot!

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closed as no longer relevant by Yemon Choi, Ryan Budney, Akhil Mathew, S. Carnahan Aug 20 '11 at 9:17

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Please do not cross-post:… Pick a site you think is appropriate and stick to it (perhaps moving if your opinion of appropriateness changes). – Qiaochu Yuan Aug 5 '11 at 21:16
I posted an answer on math.SE: – Theo Buehler Aug 5 '11 at 21:54
Since Theo has given an answer on MSE which apparently meets the OP's needs, I am voting to close this version as "no longer relevant". – Yemon Choi Aug 19 '11 at 22:29