## Derived Functor And Acyclics [closed]

Hi,

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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Please do not cross-post: math.stackexchange.com/questions/55860/… Pick a site you think is appropriate and stick to it (perhaps moving if your opinion of appropriateness changes). – Qiaochu Yuan Aug 5 2011 at 21:16
I posted an answer on math.SE: math.stackexchange.com/q/55860 – Theo Buehler Aug 5 2011 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 2011 at 22:29