Algebraization of E∞ Ring Spectra

For a commutative ring k, the homotopy category of commutative Hk-algebras (strictly unital E∞ ring spectra under the Eilenberg-Mac Lane spectrum Hk) is equivalent to the homotopy category of E∞ differential graded k-algebras. The functor from topology to algebra is a CW approximation and cellular chain functor; the inverse equivalence is constructed by Brown’s representability theorem.