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\(K_1\) of exact categories by mirror image sequences. (English) Zbl 1275.19003

In this paper the author established a presentation for the \(K_1\)-group 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, the author showed that every element of \(K_1(P)\) arises from a mirror image sequence. This provides an alternative to Nenashev’s presentation in terms of “double short exact sequences”.

MSC:

19B99 Whitehead groups and \(K_1\)
19D99 Higher algebraic \(K\)-theory
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[1] DOI: 10.1023/A:1007718422686 · Zbl 0901.19001 · doi:10.1023/A:1007718422686
[2] DOI: 10.1006/jabr.1994.1032 · Zbl 0798.19001 · doi:10.1006/jabr.1994.1032
[3] DOI: 10.1016/S0022-4049(97)00056-X · Zbl 0923.19001 · doi:10.1016/S0022-4049(97)00056-X
[4] DOI: 10.1007/s10977-004-1482-y · Zbl 1077.19003 · doi:10.1007/s10977-004-1482-y
[5] Algebraic K-Theory, Contemp. Math. 199 pp 151– (1996)
[6] DOI: 10.1016/0021-8693(79)90290-4 · Zbl 0436.18010 · doi:10.1016/0021-8693(79)90290-4
[7] Ill. J. of Math. 31 pp 574– (1987)
[8] DOI: 10.1023/A:1007722523594 · Zbl 0901.19002 · doi:10.1023/A:1007722523594
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