Algebraic K-theory and abstract homotopy theory |
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Authors: | Andrew J. Blumberg Michael A. Mandell |
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Affiliation: | aDepartment of Mathematics, The University of Texas, Austin, TX 78712, United States;bDepartment of Mathematics, Indiana University, Bloomington, IN 47405, United States |
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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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Keywords: | MSC: primary, 19D99 secondary, 55U35 |
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