G. Garkusha, “Systems of diagram categories and $K$-theory. I”, Algebra i Analiz, 18:6 (2006), 131–186; St. Petersburg Math. J., 18:6 (2007), 957

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Algebra i Analiz, 2006, Volume 18, Issue 6, Pages 131–186 (Mi aa96)

This article is cited in 4 scientific papers (total in 4 papers)

Research Papers

Systems of diagram categories and

K

$K$ -theory. I

G. Garkusha

Department of Mathematics, The University of Manchester, Manchester, UK

Full-text PDF (483 kB) Citations (4)

References:

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Abstract: With any left system of diagram categories or any left pointed dérivateur, a

K

$K$ -theory space is associated. This

K

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

K

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

K

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

K

$K$ -theory of the associated dérivateur.

Received: 06.03.2006

English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 6, Pages 957–996
DOI: https://doi.org/10.1090/S1061-0022-07-00978-8

Bibliographic databases:

Document Type: Article

MSC: 19D99

Language: Russian

Citation: G. Garkusha, “Systems of diagram categories and

K

$K$ -theory. I”, Algebra i Analiz, 18:6 (2006), 131–186; St. Petersburg Math. J., 18:6 (2007), 957–996

Citation in format AMSBIB

\Bibitem{Gar06}

\by G.~Garkusha

\paper Systems of diagram categories and $K$-theory.~I

\jour Algebra i Analiz

\yr 2006

\vol 18

\issue 6

\pages 131--186

\mathnet{http://mi.mathnet.ru/aa96}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2307357}

\zmath{https://zbmath.org/?q=an:1136.19001}

\transl

\jour St. Petersburg Math. J.

\yr 2007

\vol 18

\issue 6

\pages 957--996

\crossref{https://doi.org/10.1090/S1061-0022-07-00978-8}

Linking options:

https://www.mathnet.ru/eng/aa96

https://www.mathnet.ru/eng/aa/v18/i6/p131

This publication is cited in the following 4 articles:

George Raptis, “Higher homotopy categories, higher derivators, and K-theory”, Forum of Mathematics, Sigma, 10 (2022)
Muro F., Raptis G., “K-Theory of Derivators Revisited”, Ann. K-Theory, 2:2 (2017), 303–340
Muro F., Tonks A., Witte M., “On Determinant Functors and K-Theory”, Publ. Mat., 59:1 (2015), 137–233
Muro F., Raptis G., “A note on $K$ -theory and triangulated derivators”, Adv. Math., 227:5 (2011), 1827–1845

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	366
Full-text PDF :	114
References:	54
First page:	5

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