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Model structures for pro-simplicial presheaves

Published online by Cambridge University Press:  24 May 2011

J.F. Jardine
J.F. Jardine
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario N6A5B7, Canadajardine@uwo.ca
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Abstract

This paper displays model structures for the category of pro-objects in simplicial presheaves on an arbitrary small Grothendieck site. The first of these is an analogue of the Edwards-Hastings model structure for pro-simplicial sets, in which the cofibrations are monomorphisms and the weak equivalences are specified by comparisons of function complexes. Other model structures are built from the Edwards-Hastings structure by using Bousfield-Friedlander localization techniques. There is, in particular, an n-type structure for pro-simplicial presheaves, and also a model structure in which the map from a pro-object to its Postnikov tower is formally inverted.

Keywords

simplicial presheavespro-objectsn-typesPostnikov tower

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Type
Research Article
Information
Journal of K-Theory , Volume 7 , Issue 3 , June 2011 , pp. 499 - 525
Copyright
Copyright © ISOPP 2011

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