#### Volume 13, issue 3 (2013)

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Fibre sequences and localization of simplicial sheaves

### Matthias Wendt

Algebraic & Geometric Topology 13 (2013) 1779–1813
##### Abstract

In this paper, we discuss the theory of quasifibrations in proper Bousfield localizations of model categories of simplicial sheaves. We provide a construction of fibrewise localization and use this construction to generalize a criterion for locality of fibre sequences due to Berrick and Dror Farjoun. The results allow a better understanding of unstable ${\mathbb{A}}^{1}$–homotopy theory.

##### Keywords
Bousfield localization, simplicial sheaves, A^1-homotopy theory
##### Mathematical Subject Classification 2010
Primary: 55R65, 55P60
Secondary: 18F20, 14F42
##### Publication
Received: 25 April 2012
Revised: 6 February 2013
Accepted: 12 February 2013
Published: 19 May 2013
##### Authors
 Matthias Wendt Mathematisches Institut Albert-Ludwigs-Universität Freiburg Eckerstraße 1 D-79104, Freiburg im Breisgau Germany