Given two spectra $X,Y\in \mathrm{HoSpectra}$ we have an abelian group $[X,Y]$. What can be said about the Eilenberg-Maclane spectrum of $[X,Y]$? I think that $H[X,Y]$ would be $F(X,Y)$ the internal hom. Does anybody know where I can find this?
@AliCaglayan For any spectrum X, F(S^0,X)=X where S^0 is the sphere spectrum. So if what you say were true, all spectra would be Eilenberg-MacLane spectra. This is quite clearly false