Classifying spectra for generalized homology theories (Q1312956)

This paper gives a new proof of the classical result that every generalized homology theory on the CW-complex category has a classifying spectrum unique up to isomorphism in the Boardman homotopy category. It shunts E. H. Brown representation theorem so as \(S\)-duality and uses the fact, pointed out by the author [ibid. 155, 143-191 (1989; Zbl 0695.55005)], that each such generalized homology theory comes from a chain functor. The proof is direct and provides him with a canonical construction of the classifying spectrum, which is a Kan spectrum: this mainly contributes to the interest of the work.