  We describe the second homotopy group of any CW-complex $K$ by analyzing the
universal cover of a locally finite model of $K$ using the notion of
$G$-coloring of a partially ordered set. As applications we prove a
generalization of the Hurewicz theorem, which relates the homotopy and homology
of non-necessarily simply-connected complexes, and derive new results on
asphericity for two-dimensional complexes and group presentations.
