论文标题
通过非亚伯张量产品的内部交叉模块的通用中心扩展
Universal central extensions of internal crossed modules via the non-abelian tensor product
论文作者
论文摘要
在给定的半亚伯利亚类别中固定基本对象上的内部交叉模块的上下文中，我们使用非亚伯张量产品，以证明一个对象是完美的（从适当意义上讲），并且仅当它允许通用中心扩展时。这扩展了棕色 - 漫游的结果（对于组而言）和Edalatzadeh（对于Lie代数）。我们的目的是解释如何从分类的Galois理论来理解这些结果：Edalatzadeh在准指定类别方面的解释适用，但是基于Casas和第二作者作品中尖锐的环境中开发的理论，一种更直接的方法。
In the context of internal crossed modules over a fixed base object in a given semi-abelian category, we use the non-abelian tensor product in order to prove that an object is perfect (in an appropriate sense) if and only if it admits a universal central extension. This extends results of Brown-Loday (in the case of groups) and Edalatzadeh (in the case of Lie algebras). Our aim is to explain how those results can be understood in terms of categorical Galois theory: Edalatzadeh's interpretation in terms of quasi-pointed categories applies, but a more straightforward approach based on the theory developed in a pointed setting by Casas and the second author works as well.
