TITLE: The homotopy cofiber of the smash product of two maps of spectra
QUESTION [5 upvotes]: It is a standard fact that smashing with a fixed spectrum $Z$ preserves cofiber sequences.  So if I have a cofiber sequence $$X \xrightarrow{f} Y \rightarrow C_f$$ then there is also a cofiber sequence $$Z \wedge X \rightarrow Z \wedge Y \rightarrow Z \wedge C_f$$
If more generally I have a map $Z \xrightarrow{g} W$, is there any formula for the cofiber of the map $$Z \wedge X \xrightarrow{g \wedge f} W \wedge Y$$ in terms of $C_f$ and $C_g$?  (The above discussion corresponding to $g = \mathrm{id}_Z$).

REPLY [2 votes]: An axiomatization of exactly how smash products of cofiber sequences 
should behave is given in the context of triangulated categories in 
my paper
The additivity of traces in triangulated categories. 
Advances in Mathematics 163(2001), 34--73.
Of course, the axioms hold in the motivating example of the homotopy
category of spectra.