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Higher principal bundles

Published online by Cambridge University Press:  22 February 2006

J. F. JARDINE  and
Z. LUO
J. F. JARDINE
Affiliation:
Department of Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada.
Z. LUO
Affiliation:
Department of Mathematics, University of Haifa, 31905 Haifa, Israel. e-mail: zluo@uno.ca
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Abstract

We define torsors for sheaves of simplicial groups and sheaves of groupoids enriched in simplicial sets, and give classification results for these torsors in terms of the homotopy theory of simplicial sheaves. The proofs of the classification results use a new, general approach to cocycles taking values in simplicial sheaves. We prove a homotopy classification result for gerbes locally isomorphic to a fixed sheaf of groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 140 , Issue 2 , March 2006 , pp. 221 - 243
Copyright
2006 Cambridge Philosophical Society

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