Is there an account in English of results from "Homologie nicht-additiver Funktoren. Anwendungen" by Dold and Puppe? I am mostly interested in the spectral sequence of cross-effects which computes the homology of a functor on the suspension (p.251) and in the fact that higher symmetric powers of $K(\mathbb{Z},1)$ are null-homotopic (p.306).

For context: I am trying to understand Curtis's paper "Lower central series of semi-simplicial complexes" and it relies on results by Dold and Puppe.

Of course, I am also interested in the modern approach to similar results if there is any.