Editing Spectrum (topology) (section)

==The triangulated homotopy category of spectra==

The stable homotopy category is additive: maps can be added by using a variant of the track addition used to define homotopy groups. Thus homotopy classes from one spectrum to another form an abelian group.  Furthermore the stable homotopy category is [[triangulated category|triangulated]] (Vogt (1970)), the shift being given by suspension and the distinguished triangles by the [[Mapping cone (topology)|mapping cone]] sequences of spectra 
:<math>X\rightarrow Y\rightarrow Y\cup CX \rightarrow (Y\cup CX)\cup CY \cong \Sigma X</math>.