论文标题
组到一致关系以及从分类组到C跨模块
Groups up to congruence relation and from categorical groups to c-crossed modules
论文作者
论文摘要
我们介绍了C组的概念，该概念是一个旨在一致关系的小组，并考虑相应的类别。在此类别中定义了扩展，动作和交叉模块（C串联模块），并构建了半独立产品。我们证明，每个分类组都会产生C组和一个C串联模块，该模块在我们定义的意义上是一个连接，特殊且严格的C跨模块。此处获得的结果将用于分类组类别的等效性和连接，特殊和严格的C串联模块的证明。
We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to c-groups and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.
