Resumen de Realization of long exact sequences of abelian groups

Irwin S. Pressman

• Given a long exact sequence of abelian groups L: ... ? Li-1 ??i-1 Li ??i 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.