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Crossed modules of racks

机译:交叉的机架模块

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摘要

We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the relation between crossed modules of groups and strict 2-groups. Then we explore topological applications. We show that by applying the rackspace functor, a crossed module of racks gives rise to a covering. Our main result shows how the fundamental racks associated to links upstairs and downstairs in a covering fit together to form a crossed module of racks.
机译:我们将组的交叉模块的概念推广到机架的交叉模块的概念。我们研究了与分类的机架(即严格的2个机架)和机架类别中的行李箱状对象之间的关系,归纳了交叉的模块组和严格的2个组之间的关系。然后,我们探索拓扑应用。我们展示了通过应用机架函子,交叉的机架模块会产生覆盖。我们的主要结果表明,与楼上和楼下的链接相关联的基本机架如何通过覆盖物装配在一起以形成交叉的机架模块。

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