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!