Algebraic K-theory and abstract homotopy theory, by Andrew J. Blumberg and Michael A. Mandell

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.


Andrew J. Blumberg <blumberg@math.stanford.edu>
Michael A. Mandell <mmandell@indiana.edu>