nLab
cohomological functor

An additive functor FF from a triangulated category AA (with translation denoted XX[1]X\mapsto X[1]) to an abelian category CC is a cohomological functor if for any distinguished triangle

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

in AA, FXFfFYFgFZF X\stackrel{F f}\to F Y\stackrel{F g}\to F Z is an exact sequence in CC.

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