I am curious if something like the Nine Lemma (http://en.wikipedia.org/wiki/Nine_lemma) is true in an arbitrary triangulated category. To be more explicit, suppose I have a map of cofiber sequences/distinguished triangles and I take the cofiber/mapping cone at each stage vertically (this gives a diagram like the diagram in the wikipedia link without the zeroes) then is the bottom row a cofiber sequence/distinguished triangle?
I am particularly interested in the category of spectra if that makes things easier or harder.
Also, if the result is not true in general what about when one of the maps that we end up taking the cofiber of is the identity map?
I feel like this ought to be true but I did not see anything in the two references I checked and I am not sure how to make us of verdier's/octahedral axiom.
thanks for your time.