Holmstrom Postnikov tower

A short and beautiful exposition of Postnikov stuff and the underlying ideas is LNM0013.

A rigorous treatment is found in Jardine-Goerss chapter VI. They also discuss model structures on towers of spaces.

nLab

http://ncatlab.org/nlab/show/Postnikov+system+in+triangulated+category

Dieudonne in Panorama: The notion of fibration also enables us to characterize homotopy types by a system of invariants. Given a sequence of groups $G 1 , G 2 ,..., G n ,\ldots$ commutative for $n \geq 2$, we define a sequence of spaces $X_i$ where $X_1 = K(G_1,1)$ and $X_n$ for $n \geq 2$ is a bundle with base $X_{n - 1}$ and fiber $K(G_n , n)$. The inverse limit $X$ of the sequence $(X_n )$ is such that \pi_n (X) = G_n$ for all $n$, and every space $Y has the same homotopy type as such an inverse limit; this homotopy type is characterized by the $G_n$ and, for each $n \geq 2$, the isomorphism class of the bundle $X_n$ with base $X_{n - 1}$ ; it can be shown that these isomorphism classes are in one-one correspondence with cohomology classes in $H^{n+ 1}(X_{n-1} , G_n )$ (Postnikov’s construction).

Dwyer: Self-homotopy equivalences of Postnikov conjugates

nLab page on Postnikov tower