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arXiv · 0708.0206

Algebraic K-theory and abstract homotopy theory

Andrew J. Blumberg·Michael A. Mandell
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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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Andrew J. Blumberg, Michael A. Mandell. 2010-11-02. Algebraic K-theory and abstract homotopy theory. https://arxiv.org/abs/0708.0206

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