= Comparison of stable maps and cohomology operations
For cellular <Omega-spectra> $D,E$, natural degree-preserving additive operations $D^*\to E^*$ commuting with suspension are compatible families $[D_j,E_j]_*$ by the <Yoneda lemma>. Since $D\simeq\operatorname{hocolim}_j\Sigma^{-j}\Sigma^\infty D_j$, the <Milnor exact sequence for maps of spectra> realizes every such family. Its kernel consists precisely of <hyperphantom maps of spectra>. Thus operations determine stable maps only modulo that kernel.
Back to article page
