cohomological functor

An additive functor $F$ from a triangulated category $A$ (with translation denoted $X\mapsto X[1]$) to an abelian category $C$ is a **cohomological functor** if for any distinguished triangle

$X\stackrel{f}\to Y\stackrel{g}\to Z\stackrel{h}\to X[1],$

in $A$, $F X\stackrel{F f}\to F Y\stackrel{F g}\to F Z$ is an exact sequence in $C$.

Last revised on March 30, 2009 at 12:29:11. See the history of this page for a list of all contributions to it.