论文标题
广义交叉模块的覆盖物和抬起
Coverings and liftings of generalized crossed modules
论文作者
论文摘要
在交叉模块的理论中，考虑任意的自我行为而不是共轭可以扩展交叉模块的概念，因此出现了广义交叉模块的概念。在本文中，我们为广义CAT $^1 $ group提供了一个精确的定义，并从广义CAT $^1 $ groups的类别中获取函数到通用交叉模块。此外，我们介绍了通用交叉模块的覆盖和举起的概念，并研究了这些结构的特性。这项研究的主要目的是获得覆盖类别的类别与给定的广义交叉模块$（a，b，α）$的升降类别之间的等效性。
In the theory of crossed modules, considering arbitrary self-actions instead of conjugation allows for the extension of the concept of crossed modules and thus the notion of generalized crossed module emerges. In this paper we give a precise definition for generalized cat$^1$-groups and obtain a functor from the category of generalized cat$^1$-groups to generalized crossed modules. Further, we introduce the notions of coverings and liftings for generalized crossed modules and investigate properties of these structures. Main objective of this study is to obtain an equivalence between the category of coverings and the category of liftings of a given generalized crossed module $(A,B,α)$.
