nLab
cohomological functor

An additive functor F from a triangulated category A (with translation denoted XX[1]) to an abelian category C 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 A, FXFfFYFgFZ is an exact sequence in C.

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