An algebraic proof of Quillen's resolution theorem for K1

Ben Whale

doi:10.1017/is009009019jkt089

An algebraic proof of Quillen's resolution theorem for K₁

Ben Whale^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	115-144
Number of pages	30
Journal	Journal of K-Theory
Volume	7
Issue number	1
DOIs	https://doi.org/10.1017/is009009019jkt089
Publication status	Published - Feb 2011

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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.",

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KW - Resolution Theorem

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An algebraic proof of Quillen's resolution theorem for K₁

Abstract

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