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.


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