BibTeX
@MISC{Crans95quillenclosed,
author = {Sjoerd E. Crans},
title = {Quillen Closed Model Structures for Sheaves},
year = {1995}
}
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Abstract
In this chapter 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. 1 Introduction There are two ways of trying to generalize the well known closed model structure on the category of simplicial sets to the category of simplicial objects in a Grothendieck topos. One way is to concentrate on the local aspect, and to use the Kan-fibrations as a starting point. In [14] Heller showed that for simplicial presheaves there is a local (there called right) closed model structure. In [2] K. Brown showed that for a topological space X the category of "locally fibrant" sheaves of spectra on ...
Keyphrases
model structure simplicial sheaf closed model structure homotopy theory simplicial presheaves starting point bisimplicial sheaf global closed model structure simplicial object adjoint functor pair grothendieck topos topological space fibrant sheaf local aspect simplicial set general procedure
