Hostname: page-component-7bb8b95d7b-495rp Total loading time: 0 Render date: 2024-09-18T13:27:19.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Quotients of groupoids by an action of a group

Published online by Cambridge University Press:  24 October 2008

John Taylor
John Taylor
Affiliation:
Department of Mathematics, University of the West Indies, Mona, Kingston 7, Jamaica, West Indies
Get access Rights & Permissions [Opens in a new window]

Extract

For any category A and group G there is a category AG of A-objects with G-action. An object of AG is an A-object A together with a group morphism, θA:G → Isom (A, A), of G into the group of invertible A-morphisms A → A. A morphism of AG is an A-morphism f: A → B which commutes with the G-action; that is, for each g∈G, the following diagram commutes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 2 , March 1988 , pp. 239 - 249
Copyright
Copyright © Cambridge Philosophical Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Armstrong, M. A.. On the fundamental group of an orbit space. Proc. Cambridge Philos. Soc. 61 (1965), 639–646.CrossRefGoogle Scholar
[2]Armstrong, M. A.. The fundamental group of the orbit space of a discontinuous group. Proc. Cambridge Philos. Soc. 64 (1968), 299–301.CrossRefGoogle Scholar
[3]Armstrong, M. A.. Calculating the fundamental group of an orbit space. Proc. Amer. Math. Soc. 84 (1982), 267–271.CrossRefGoogle Scholar
[4]Armstrong, M. A.. Lifting homotopies through fixed points. Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 123–128.Google Scholar
[5]Armstrong, M. A.. Lifting homotopies through fixed points II. Proc. Roy. Soc. Edinburgh Sect. A 96 (1984), 201–205.Google Scholar
[6]Brown, R.. Elements of Modern Topology (McGraw-Hill, 1968), 2nd Edition (Ellis Horwood, to appear).Google Scholar
[7]Brown, R.. Fibrations of groupoids. J. Algebra 15 (1970), 103–132.CrossRefGoogle Scholar
[8]Brown, R.. Groupoids as coefficients. Proc. London Math. Soc. (3) 25 (1972), 413–426.CrossRefGoogle Scholar
[9]Brown, R.. From groups to groupoids: a brief survey. Bull. London Math. Soc. 19 (1987), 113–134.CrossRefGoogle Scholar
[10]Brown, R. and Danesh-Naruie, G.. The fundamental groupoid as a topological groupoid. Proc. Edinburgh Math. Soc. 19 (1974), 237–244.CrossRefGoogle Scholar
[11]Brown, R. and Higgins, P. J.. On the fundamental groupoid of an orbit space. U.C.N.W. Preprint (1987).Google Scholar
[12]Ehresmann, C.. Oeuvres complètes et commentées. Ed. Andrée C. Ehresmann, Suppl. 1, 2.Cah. Top. Géom. Diff. 24 (1983) Parties 1–1, 1–2.Google Scholar
[13]Higgins, P. J.. Presentations of groupoids, with applications to groups. Proc. Cambridge Philos. Soc. 60 (1964), 7–20.CrossRefGoogle Scholar
[14]Higgins, P. J.. Categories and groupoids. Van Nostrand Mathematical Studies 32 (Van Nostrand, 1971).Google Scholar
[15]Higgins, P. J. and Taylor, J.. The fundamental groupoid and homotopy crossed complex of an orbit space. In Category Theory: Proceedings Gummersbach 1981, ed. Kamps, K. H. et al. , Lecture Notes in Math. vol. 962 (Springer-Verlag, 1982), pp. 115–122.CrossRefGoogle Scholar
[16]Mackey, G. W.. Ergodic theory and virtual groups. Math. Ann. 166 (1966), 187–207.CrossRefGoogle Scholar
[17]Salleh, A. Razak and Taylor, J.. On the relation between the fundamental groupoids of the classifying space and the nerve of an open cover. J. Pure Appl. Algebra 37 (1985), 81–93.CrossRefGoogle Scholar
[18]Rhodes, F.. On the fundamental group of a transformation group. Proc. London Math. Soc. (3) 16 (1966), 635–650.CrossRefGoogle Scholar
[19]Taylor, J.. Group actions on ω-groupoids and crossed complexes, and the homotopy groups of orbit spaces. Ph.D. thesis, University of Durham (1982).Google Scholar