The functors mapping
cone, Cf, and its dual, Ef, whose definitions will be recalled below, seem to
have been introduced by Puppe and Nomura in 1958 and 1960 respectively.
There, various basic properties of these functors were established. Here we
shall prove a ‘3 × 3 lemma” for the functor Ef (with an obvious dual for
Cf). This will be applied in §3 to the problem of determining a Postnikov
system for Ef in terms of f, and to show that any space having a Postnikov
decomposition, and whose homotopy is finitely generated, has a decomposition in
which the only K(π,n)’s appearing have π a finitely generated free abelian
group.
