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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Systems of diagram categories and $ K$-theory. I


Author: G. Garkusha
Original publication: Algebra i Analiz, tom 18 (2006), nomer 6.
Journal: St. Petersburg Math. J. 18 (2007), 957-996
MSC (2000): Primary 19D99
DOI: https://doi.org/10.1090/S1061-0022-07-00978-8
Published electronically: October 2, 2007
MathSciNet review: 2307357
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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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Additional Information

G. Garkusha
Affiliation: Department of Mathematics, University of Wales Swansea, Singleton Park, SA2 8PP Swansea, United Kingdom
Email: garkusha@imi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-07-00978-8
Keywords: Systems of diagram categories, Grothendieck's d\'erivateurs, algebraic $K$-theory
Received by editor(s): March 8, 2006
Published electronically: October 2, 2007
Additional Notes: Supported by the ICTP Research Fellowship
Article copyright: © Copyright 2007 American Mathematical Society

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