Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-25T21:55:59.945Z Has data issue: false hasContentIssue false

On the cohomology of local groups

Published online by Cambridge University Press:  09 April 2009

S. Świerczkowski
Affiliation:
Australian National UniversityCanberra
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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), 336343.CrossRefGoogle Scholar
[2]Barr, M. and Beck, J., Homology and standard constructions (Lecture Notes No. 80, Springer, Berlin, 1969, 245335).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), 391408.CrossRefGoogle Scholar
[5]MacLane, Saunders, Homology (Springer, Berlin, 1963).CrossRefGoogle Scholar
[6]MacLane, Saunders, ‘Categorical algebra’, Bull. Amer. Math. Soc. 71 (1965), 40106.CrossRefGoogle Scholar
[7]Malcev, A. I., ‘Sur les groupes topologiques locaux et complets’, C. R. (Doklady) Acad. Sci. URSS (N.S) 32 (1941), 606608.Google Scholar
[8]Seminar on triples and categorical homology theory (Lecture Notes No. 80, Springer, Berlin, 1969).Google Scholar