On Representable Half-Exact Functors over B

Abstract

Half-exact homotopy functors defined on categories over a fixed base space B generalize cohomology functors with local coefficients. It is proved that such functors, if strongly homotopy invariant, are representable in the sense of EJI. Brown by fiber spaces E → B. The result is a consequence of a reformulation of his fundamental representation theorem in the abstract homotopy theory.