ABSTRACT
In Chapter 7 we explore the category CSA of “coherent sequences of algebras” and we prove several results of a formal nature about them. A csa is a device for handling simultaneously the homology or homotopy groups with coefficients in Zp, in Zp2, in Zp3, and so on. The language and properties of the csa’s will be essential for stating and proving many of the properties of the spaces Dk and Ek-
The standard tool for working simultaneously with torsion of all orders is the Bockstein spectral sequence. However, it turns out that the BSS has too much indeterminacy built into it for the applications we have in mind. We are led to seek a structure that has all the information in the BSS but which also keeps some the information about how to mulitply and divide by p. We especially need it to accommodate easily to work with mod p1 homotopy classes, for t > 1. The device that meets these requirements is the coherent sequence of algebras, or, as appropriate, the coherent sequence of Lie algebras.
