Fibre sequences and localization of simplicial sheaves
Matthias Wendt
TL;DR
This paper develops a theory of quasi-fibrations and fiberwise localization in localized model categories of simplicial sheaves, enhancing understanding of unstable A^1-homotopy theory.
Contribution
It introduces a new construction of fiberwise localization and generalizes a criterion for the locality of fiber sequences in simplicial sheaves.
Findings
Provides a construction of fiberwise localization in proper Bousfield localizations.
Generalizes a criterion for the locality of fiber sequences.
Improves understanding of unstable A^1-homotopy theory.
Abstract
In this paper, we discuss the theory of quasi-fibrations 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 result allows a better understanding of unstable A^1-homotopy theory.
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