For a triangulated category, given a map between two morphisms, there is a morphism between their mapping cones (which exist by axiom (TR 1)), that makes everything commute. This means that in this diagram (where f and g form the map of morphisms) there exists some map h (not necessarily unique) making all the squares commute.
en:Image:Triangle diagram.jpg
en:User:Ryan Reich, User:Stannered