St. Petersburg Mathematical Society

Author(s): 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
Posted: October 2, 2007
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Abstract: With any left system of diagram categories or any left pointed dérivateur, a

-theory space is associated. This

-theory space is shown to be canonically an infinite loop space and to have a lot of common properties with Waldhausen's

-theory. A weaker version of additivity is shown. Also, Quillen's

-theory of a large class of exact categories including the Abelian categories is proved to be a retract of the

-theory of the associated dérivateur.

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

DOI: 10.1090/S1061-0022-07-00978-8
PII: S 1061-0022(07)00978-8
Keywords: Systems of diagram categories, Grothendieck's d\'erivateurs, algebraic $K$-theory
Received by editor(s): 8/MAR/2006
Posted: October 2, 2007
Additional Notes: Supported by the ICTP Research Fellowship
Copyright of article: Copyright 2007, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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