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An Algebraic Proof of Quillen's Resolution Theorem for K1

Published online by Cambridge University Press:  02 October 2009

Ben Whale
Ben Whale
Affiliation:
Centre for Gravitational Physics, Department of Quantum Science, College of Physical Sciences, The Australian National University, Canberra, ACT 0200, Australia, [email protected].
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Abstract

In his 1973 paper [4] Quillen proved a resolution theorem for the K-Theory of an exact category; his proof was homotopic in nature. By using the main result of Nenashev's paper [3], we are able to give an algebraic proof of Quillen's Resolution Theorem for K1 of an exact category. We view this as an advance towards the goal of giving an essentially algebraic subject an algebraic foundation.

Keywords

Resolution TheoremK-TheoryExact Category
Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 1 , February 2011 , pp. 115 - 144
Copyright
Copyright © ISOPP 2009

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References

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3.Nenashev, Alexander. Double short exact sequences and K 1 of an exact category. K-Theory, 14(1):23–41, 1998.CrossRefGoogle Scholar
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