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On the correspondence between gerbes and bouquets

Published online by Cambridge University Press:  24 October 2008

K.-H. Ulbrich
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki 305, Japan

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
Copyright
Copyright © Cambridge Philosophical Society 1990

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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), 165191.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