Israel Journal of Mathematics

, Volume 163, Issue 1, pp 93–124 | Cite as

A homotopy theory for stacks



We give a homotopy theoretic characterization of stacks on a site C as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category in which stacks are the fibrant objects. We compare different definitions of stacks and show that they lead to Quillen equivalent model categories. In addition, we show that these model structures are Quillen equivalent to the S2-nullification of Jardine’s model structure on sheaves of simplicial sets on C.


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Copyright information

© The Hebrew University of Jerusalem 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat RamThe Hebrew University of Jerusalem JerusalemIsrael
  2. 2.Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Mathema’ticaInstituto Superior Te’cnicoLisboaPortugal

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