A homotopy theory for stacks |
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| Authors: | Sharon Hollander |
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| Institution: | (1) Department of Mathematics, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem Jerusalem, 91904, Israel;(2) Present address: Center for Mathematical Analysis, Geometry, and Dynamical Systems, Departamento de Mathema’tica, Instituto Superior Te’cnico, 1049-001 Lisboa, Portugal |
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| Abstract: | 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 S
2-nullification of Jardine’s model structure on sheaves of simplicial sets on C. |
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