Description
This paper is devoted to formulating an introduction to the study of (homology) spectral sequences in topology. A spectral sequence is a homological device for relating the homology of a pair of abelian objects to that of a third object. In the past twenty years, these constructions have proved useful in both algebraic topology and in the cohomology of groups. Yet, their development has been fragmentary and generally inaccessible to all but those specializing in this area. A purpose of this paper is to unify this theory around a few key theorems which we have formulated into a categorical framework, and provide a setting from which some simplifications of proofs can be made. In particular, such sequences as the Wang, Gysin, and Serre homology sequences are easy consequences of Serre's Theorem and Leray-Serre Theorem. Much of the paper is devoted to the construction of the following categories and functors and to show a natural equivalence between F•G and E. We have also supplied a reasonably thorough bibliography.
