Quillen closed model structures for sheaves

J. Pure Appl. Algebra 101 (1995), 35-57
also Chapter 1 of my Ph.D. thesis ``On combinatorial models for higher dimensional homotopies'', 1995, xxii+163+XV pp.

Abstract:

In this chapter/paper I give a general procedure of transferring closed model structures along adjoint functor pairs. As applications I derive from a global closed model structure on the category of simplicial sheaves closed model structures on the category of sheaves of 2-groupoids, the category of bisimplicial sheaves and the category of simplicial sheaves of groupoids. Subsequently, the homotopy theories of these categories are related to the homotopy theory of simplicial sheaves.

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Sjoerd E. Crans
Mathematical Institute
Utrecht University
Utrecht
The Netherlands