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On cocycle bitorsors and gerbes over a Grothendieck topos

Published online by Cambridge University Press:  24 October 2008

K.-H. Ulbrich
K.-H. Ulbrich
Affiliation:
Département de Mathématiques, Université Paris-Nord, C.S.P., Av. J.-B. Clément, 93430 Villetaneuse, France
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Extract

The aim of this paper is to give a new description of Giraud's nonabelian cohomology set H2(L), [7], defined for a band L of a Grothendieck topos E as the set of L-equivalence classes of L-gerbes over E. Our description is similar to that for H1 by Čech cohomology, but with cocycles taken from the stack of bitorsors over E. We first continue to study the construction of gerbes by cocycle bitorsors or bouquets [13], originally given in [7] and [4]; Duskin [4, 5] showed that bouquets B and B′ of E give rise to equivalent gerbes if and only if there exist essential equivalences B″ → B and B″ → B′ for another bouquet B″.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 49 - 55
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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