We set up machinery for recognizing –cellular modules and –cellular approximations, where is an –module and 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.
"Cellular approximations and the Eilenberg–Moore spectral sequence." Algebr. Geom. Topol. 9 (3) 1309 - 1340, 2009. https://doi.org/10.2140/agt.2009.9.1309