An Algebraic Proof of Quillen's Resolution Theorem for K_1

TL;DR

This paper provides an algebraic proof of Quillen's Resolution Theorem for K_1 in exact categories, offering an alternative to the original homotopic proof and leveraging recent algebraic results.

Contribution

It introduces an algebraic proof of Quillen's K_1 resolution theorem, expanding the methods used in algebraic K-theory.

Findings

Algebraic proof of Quillen's Resolution Theorem for K_1

Utilizes recent results by Nenashev to simplify the proof

Provides an alternative approach to homotopic proofs in K-theory

Abstract

In his 1973 paper 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 a paper by Nenashev, we are able to give an algebraic proof of Quillen's Resolution Theorem for K_1 of an exact category.