nLab triangulated functor

Idea

A triangulated functor $F : T \to T'$ between two triangulated categories $T$ and $T'$ is an additive functor that commutes with translation and preserves the distinguished triangles.

(Neeman 01, def. 2.1.1)

Triangulated functors are also called exact functors (not to be confused with the other meaning of exact functor).

Related concepts

• tensor triangulated category

• Fourier-Mukai transform

References

• Amnon Neeman, Triangulated Categories, Princeton University Press (2001)