Stable homotopy category ($[D,E{]}_{\mathrm{st}}$)

The stable homotopy category is obtained from topological spectra by inverting stable equivalences of spectra. Its morphisms are abelian groups; for a cellular source and fibrant target they are spectrum homotopy classes of point-set maps of topological spectra.

A map of topological spectra inducing isomorphisms on every stable homotopy group is a stable equivalence of spectra.