most recent 30 from http://mathoverflow.net 2013-05-21T19:51:13Z http://mathoverflow.net/feeds/question/72196 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/72196/derived-functor-and-acyclics Descartes 2011-08-05T17:07:07Z 2011-08-19T21:56:17Z

<p>Hi,</p> <p>I'm not sure how I can show the following:</p> <p>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:</p> <p>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 $D^{+}(B)$.</p> <p>I don't want to assume the existence of F-adapted classes or enough Injectives, just the Existence of RF.</p> <p>Thanks a lot!</p>