  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.
