Cellular approximations and the Eilenberg–Moore spectral sequence

Abstract

We set up machinery for recognizing $k$–cellular modules and $k$–cellular approximations, where $k$ is an $R$–module and $R$ is either a ring or a ring-spectrum. Using this machinery we can identify the target of the Eilenberg–Moore cohomology spectral sequence for a fibration in various cases. In this manner we get new proofs for known results concerning the Eilenberg–Moore spectral sequence and generalize another result.