  We decompose the K-theory space of a Waldhausen category in terms of its
Dwyer-Kan simplicial localization. This leads to a criterion for functors to
induce equivalences of K-theory spectra that generalizes and explains many of
the criteria appearing in the literature. We show that under mild hypotheses, a
weakly exact functor that induces an equivalence of homotopy categories induces
an equivalence of K-theory spectra.
