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Systems of Diagram Categories and K-theory I

Grigory Garkusha
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Abstract

To any left system of diagram categories or to any left pointed derivateur (in the sense of Grothendieck) a K-theory space is associated. This K-theory space is shown to be canonically an infinite loop space and to have a lot of common properties with Waldhausen's K-theory. A weaker version of additivity is shown. Also, Quillen's K-theory of a large class of exact categories including the abelian categories is proved to be a retract of the K-theory of the associated derivateur.

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Grigory Garkusha. 2004-05-05. Systems of Diagram Categories and K-theory I. https://arxiv.org/abs/math/0401062

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