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arXiv · 2207.09702

Non-existence of fiberwise localization for crossed modules

Olivia Monjon·Jérôme Scherer·Florence Sterck
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Abstract

We prove that localization functors of crossed modules of groups do not always admit fiberwise (or relative) versions. To do so we characterize the existence of a fiberwise localization by a certain normality condition and compute explicit examples and counter-examples. In fact, some nullification functors do not behave well and we also prove that the fiber of certain nullification functors, known as acyclization functors in other settings such as groups or spaces, is not acyclic.

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Olivia Monjon, Jérôme Scherer, Florence Sterck. 2022-07-20. Non-existence of fiberwise localization for crossed modules. https://arxiv.org/abs/2207.09702

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