Realization of long exact sequences of abelian groups
- Autores: Irwin S. Pressman
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 34, Nº 1, 1990, págs. 67-76
- Idioma: inglés
- DOI: 10.5565/publmat_34190_05
- Títulos paralelos:
- Realización de sucesiones de longitud exacta de grupos abelianos
- Enlaces
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Resumen
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.
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