Non-existence of fiberwise localization for crossed modules
Category Theory
2022-10-31 v2 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.2207.09702,
title = {Non-existence of fiberwise localization for crossed modules},
author = {Olivia Monjon and Jérôme Scherer and Florence Sterck},
journal= {arXiv preprint arXiv:2207.09702},
year = {2022}
}
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19 pages