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k1

Journal of K-Theory (1)

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K1 of Exact Categories by Mirror Image Sequences
Clayton Sherman
Journal:

Journal of K-Theory / Volume 11 / Issue 1 / February 2013

Published online by Cambridge University Press:

19 April 2012, pp. 155-181

Print publication:

February 2013
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We establish a presentation for K1 of any small exact category P, based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K1(P) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”