A homotopy theory for stacks

Sharon Hollander

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

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.

Original languageEnglish
Pages (from-to)93-124
Number of pages32
JournalIsrael Journal of Mathematics
Volume163
DOIs
StatePublished - 1 Jan 2008
Externally publishedYes

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