Systems of diagram categories and 𝐾-theory. I

Garkusha, G.

doi:10.1090/S1061-0022-07-00978-8

Systems of diagram categories and $K$-theory. I
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by G. Garkusha

St. Petersburg Math. J. 18 (2007), 957-996

DOI: https://doi.org/10.1090/S1061-0022-07-00978-8

Published electronically: October 2, 2007

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Abstract:

With any left system of diagram categories or any left pointed dérivateur, 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 dérivateur.

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