Geodesic
Systems of diagram categories and $K$-theory.~I
Algebra i analiz, Tome 18 (2006) no. 6, pp. 131-186.

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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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G. Garkusha. Systems of diagram categories and $K$-theory.~I. Algebra i analiz, Tome 18 (2006) no. 6, pp. 131-186. http://geodesic.mathdoc.fr/item/AA_2006_18_6_a1/

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