When Moore-Postnikov
towers for fibrations p : E → X were first developed, Moore constructed the tower for
arbitrary maps p and, when all action on πn (fiber) were trivial, showed that each
stage was induced from the loop-path fibration over a K(π,n) and classified by the
corresponding k-invariant. Barratt-Gugenheim-Moore showed that without
restriction each stage could be induced from suitable universal fibrations.
Subsequent authors, including McClendon, Nussbaum, Robinson and Siegal,
based on the above and work by Olum, described the classifying map by
k-invariant and local coefficients when π1(X) acts and π1 (fiber) is Abelian,
and Bousfield and Kan described the case when π1 acts nilpotently. This
note gives a method for handling fibrations requiring only that all spaces be
path-connected.
