Given a long exact sequence of abelian groups
L: ... → Li-1 →ξi-1 Li →ξi Li+1 → ...
a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized. Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories are themselves abelian.
@article{urn:eudml:doc:41114,
title = {Realization of long exact sequences of abelian groups.},
journal = {Publicacions Matem\`atiques},
volume = {34},
year = {1990},
pages = {67-76},
zbl = {0713.18007},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41114}
}
Pressman, Irwin S. Realization of long exact sequences of abelian groups.. Publicacions Matemàtiques, Tome 34 (1990) pp. 67-76. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41114/