On cocycle bitorsors and gerbes over a Grothendieck topos
Published online by Cambridge University Press: 24 October 2008
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
References
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