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 $A$, $FX\stackrel{Ff}{\to}FY\stackrel{Fg}{\to}FZ$ is an exact sequence in $C$.

Revised on March 30, 2009 12:29:11
by Toby Bartels
(12.25.143.142)