Cellular approximations and the Eilenberg-Moore spectral-sequence

TL;DR

This paper develops a framework for cellular approximations in algebraic topology, enabling new insights and proofs related to the Eilenberg-Moore spectral sequence for fibrations.

Contribution

It introduces machinery to recognize and construct k-cellular modules and approximations, generalizing and providing new proofs for existing results in spectral sequence theory.

Findings

Identifies the target of the Eilenberg-Moore spectral sequence in various cases

Provides new proofs for known results in spectral sequence analysis

Generalizes previous results in the context of cellular modules

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.