Realization of long exact sequences of abelian groups.

@article{Pressman1990,
abstract = {Given a long exact sequence of abelian groupsL: ... → 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.},
author = {Pressman, Irwin S.},
journal = {Publicacions Matemàtiques},
keywords = {Teoría de grupos; Grupos; Grupos abelianos; category of abelian groups; cohomology of complexes; cohomology sequence of a short exact sequence of complexes of abelian groups; long exact sequence of abelian groups; bicartesian squares},
language = {eng},
number = {1},
pages = {67-76},
title = {Realization of long exact sequences of abelian groups.},
url = {http://eudml.org/doc/41114},
volume = {34},
year = {1990},
}

TY - JOUR
AU - Pressman, Irwin S.
TI - Realization of long exact sequences of abelian groups.
JO - Publicacions Matemàtiques
PY - 1990
VL - 34
IS - 1
SP - 67
EP - 76
AB - Given a long exact sequence of abelian groupsL: ... → 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.
LA - eng
KW - Teoría de grupos; Grupos; Grupos abelianos; category of abelian groups; cohomology of complexes; cohomology sequence of a short exact sequence of complexes of abelian groups; long exact sequence of abelian groups; bicartesian squares
UR - http://eudml.org/doc/41114
ER -