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Simplicial presheaves as stacks

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Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)


The purpose of this second lecture is to present the homotopy theory of simplicial presheaves on a Grothendieck site and explain how these are models for stacks.


  • Model Category
  • Homotopy Category
  • Lift Property
  • Twisted Form
  • Grothendieck Topology

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Correspondence to Ieke Moerdijk .

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Moerdijk, I., Toën, B. (2010). Simplicial presheaves as stacks. In: Simplicial Methods for Operads and Algebraic Geometry. Advanced Courses in Mathematics - CRM Barcelona. Springer, Basel.

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