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On the cohomology of local groups

Published online by Cambridge University Press:  09 April 2009

S. Świerczkowski
S. Świerczkowski
Affiliation:
Australian National UniversityCanberra
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Most known homology theories (e.g. the homology of modules, rings, groups, sheaves, …) have been found to be special cases of a general theory proposed by M. Barr and J. Beck [1], [2]. The aim of this paper is to show that the cohomology of a local group, as defined by W. T. van Est [4], also fits the scheme of Barr and Beck. At the same time it will be shown that local group cohomology is a relative derived functor in the sense of S. Eilenberg and J. C. Moore [3].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 2 , May 1971 , pp. 249 - 255
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Barr, M. and Beck, J., ‘Acyclic models and triples’, Proc. Conference on Categorical Algebra La Jolla 1965, (Springer, Berlin, 1966), 336–343.CrossRefGoogle Scholar
[2]Barr, M. and Beck, J., Homology and standard constructions (Lecture Notes No. 80, Springer, Berlin, 1969, 245–335).Google Scholar
[3]Eilenberg, S. and Moore, T. C., Foundations of relative homological algebra (Memoirs of the Amer. Math. Soc. No. 55, 1965).CrossRefGoogle Scholar
[4]van Est, W. T., ‘Local and global groups I’, Indag. Math. 24 (1962), 391–408.CrossRefGoogle Scholar
[5]MacLane, Saunders, Homology (Springer, Berlin, 1963).CrossRefGoogle Scholar
[6]MacLane, Saunders, ‘Categorical algebra’, Bull. Amer. Math. Soc. 71 (1965), 40–106.CrossRefGoogle Scholar
[7]Malcev, A. I., ‘Sur les groupes topologiques locaux et complets’, C. R. (Doklady) Acad. Sci. URSS (N.S) 32 (1941), 606–608.Google Scholar
[8]Seminar on triples and categorical homology theory (Lecture Notes No. 80, Springer, Berlin, 1969).Google Scholar