nLab 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 $C$.