论文标题
交叉模块的光纤定位不存在
Non-existence of fiberwise localization for crossed modules
论文作者
论文摘要
我们证明，组交叉模块的定位函数并不总是允许纤维（或相对）版本。为此，我们通过特定正态性条件并计算明确的例子和反例来表征光纤定位的存在。实际上，某些无效的函子的行为不佳，我们还证明某些无效函子的纤维，在其他设置（例如组或空间）中称为循环函数的纤维不是无环的。
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.
