K1 of exact categories by mirror image sequences
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.
Algebraic K-theory, double short exact sequence, K1, mirror image sequence
Sherman, Clayton. "K1 of Exact Categories by Mirror Image Sequences." Journal of K--Theory 11, no. 1 (2013).
Journal of K-Theory