Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T13:56:18.220Z Has data issue: false hasContentIssue false
  • English
  • Français

On the correspondence between gerbes and bouquets

Published online by Cambridge University Press:  24 October 2008

K.-H. Ulbrich
K.-H. Ulbrich
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305, Japan
Get access Rights & Permissions [Opens in a new window]

Extract

Duskin [1, 2] showed that gerbes over a Grothendieck topos E can be interpreted by certain internal groupoids of E which he called bouquets. He proved that for any bouquet B of E the fibred category F ors(B) of B-torsors is a gerbe over E, and conversely that any gerbe G gives rise to a bouquet B satisfying G ≅ F ors(B). We want to give here a somewhat different approach to these results, based on a construction of gerbes given in [3].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 1 , July 1990 , pp. 1 - 5
Copyright
Copyright © Cambridge Philosophical Society 1990

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]Duskin, J.. An outline of non-abelian cohomology in a topos. I. The theory of bouquets and gerbes. Cahiers Topologie Geom. Différentielle Catégoriques 23 (1982), 165–191.Google Scholar
[2]Duskin, J.. Non-abelian cohomology in a topos. Mem. Amer. Math. Soc. (To appear.)Google Scholar
[3]Giraud, J.. Cohomologie non Abélienne (Springer-Verlag, 1971).CrossRefGoogle Scholar
[4]Johnstone, P. T.. Topos Theory (Academic Press, 1977).Google Scholar