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On diagram-chasing in double complexes

##
George M. Bergman

We construct, for any double complex in an abelian
category, certain ``short-distance''
maps, and an exact sequence involving these, instances of
which can be pieced together to give the
``long-distance'' maps and exact sequences
of results such as the Snake Lemma.
Further applications are given.
We also note what the building
blocks of an analogous study of triple complexes would be.

Keywords:
double complex, exact sequence, diagram-chasing,
Salamander Lemma, total homology, triple complex

2000 MSC:
Primary: 18G35.
Secondary: 18E10

*Theory and Applications of Categories,*
Vol. 26, 2012,
No. 3, pp 60-96.

Published 2012-02-08.

http://www.tac.mta.ca/tac/volumes/26/3/26-03.dvi

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