Algebraic K-theory and abstract homotopy theory

@article{Blumberg2007AlgebraicKA,
  title={Algebraic K-theory and abstract homotopy theory},
  author={Andrew J. Blumberg and Michael A. Mandell},
  journal={Advances in Mathematics},
  year={2007},
  volume={226},
  pages={3760-3812}
}
Abstract 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. 
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