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Morita equivalence for continuous groups

Published online by Cambridge University Press:  24 October 2008

Ieke Moerdijk
Ieke Moerdijk
Affiliation:
Mathematical Institute, University of Amsterdam
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Extract

This paper is essentially concerned with the following problem. Let G be a topological group. AG-set is a set S equipped with a continuous action (where S is given the discrete topology). These G-sets form a category BG. It is well known that if G and H are discrete groups, BG is equivalent to BH iff G is isomorphic to H. However, this result cannot be extended much beyond the discrete case. The problem is: when is BG equivalent to BH, for topological groups G and H?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 1 , January 1988 , pp. 97 - 115
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Barr, M. and Diaconescu, R.. Atomic toposes. J. Pure Appl. Alg. 17 (1980), 1–24.CrossRefGoogle Scholar
[2]Bass, H.. Algebraic K-theory (Benjamin, 1968).Google Scholar
[3]Bénabou, J.. Introduction to bicategories, in Reports of the Midwest Category Seminar, Lecture Notes in Math. vol. 47 (Springer-Verlag, 1967), pp. 1–77.CrossRefGoogle Scholar
[4]Grothendieck, A.. Revêtements étales el groupe fondamentale. Lecture Notes in Math. vol. 224 (Springer-Verlag, 1971).CrossRefGoogle Scholar
[5]Isbell, J. R.. Atomless parts of spaces. Math. Scand. 31 (1972), 5–32.CrossRefGoogle Scholar
[6]Isbell, J. R.. Direct limits of meet-continuous lattices. J. Pure Appl. Alg. 23 (1982), 33–35.CrossRefGoogle Scholar
[7]Johnstone, P. T.. Factorization theorems for geometric morphisms I. Cahiers Top. Géom. Diff. 22 (1981), 3–17.Google Scholar
[8]Johnstone, P. T.. Stone Spaces (Cambridge University Press, 1982).Google Scholar
[9]Joyal, A. and Tierney, M.. An extension of the Galois theory of Grothendieck. Memoirs Amer. Math. Soc. 309 (1984).Google Scholar
[10]Moerdijk, I.. Continuous fibrations and inverse limits of Grothendieck toposes. Compositio Math. 58 (1986), 45–72.Google Scholar
[11]Moerdijk, I.. Prodiscrete groups, to appear (preprint: University of Amsterdam. Mathematics report 86–22).Google Scholar
[12]Moerdijk, I.. The classifying topos of a continuous groupoid, to appear in Trans. Amer. Math. Soc. (preprint: University of Amsterdam, Mathematics report 86–27).Google Scholar
[13]Moerdijk, I. and Wraith, G. C.. Connected locally connected toposes are path-connected. Trans. Amer. Math. Soc. 295 (1986), 849–859.CrossRefGoogle Scholar
[14]Morita, K.. Duality of modules and its applications to the theory of rings with minimum condition. Sci. Rep. Tokyo Kyokiu Daigaku 6 Ser. A (1958), 83–142.Google Scholar