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The K -theory of rings can be defined in terms of nonabelian derived functors as described in Nonabelian derived functors and algebraic K-theory. Springer, 1973; see also the books Algebraic K-theory. Kluwer Academic Publishers Group, 1995 and Non-abelian homological algebra and its applications. Kluwer Academic Publishers, 1997 of Inassaridze for a similar approach. In fact both Swan's theory and Quillen's theory can be described this way. The equivalence of both K -theories is proved by Gersten Comm. Algebra 1: 39–64, 1974. In this paper we give a proof using these descriptions that involve nonabelian derived functors.
Georgian Mathematical Journal – de Gruyter
Published: Dec 1, 2002
Keywords: Higher algebraic K -theory; simplicial resolutions
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