论文标题
有条件的平坦度，纤维定位和可允许的反射
Conditional flatness, fiberwise localizations, and admissible reflections
论文作者
论文摘要
我们将本地化函数的条件平坦度的群体理论概念扩展到任何尖锐的类别，并在同源类别和半阿伯式类别的背景下进行调查。在存在函数纤维定位的情况下，类似于组中所获得的结果的结果，我们为特定的半亚洲类别中某些定位函数提供了存在定理。我们证明，理想确定类别的Birkhoff子类别产生了有条件的定位，并解释了条件平坦的含量与从分类Galois理论的角度相对应的邻接的可接受性。在纤维定位的假设下，我们给出了一个简单的标准，以确定何时（正常EPI）反射是无扭转的反射。这表明这特别适用于任何半亚伯式的通用代数中的无效函子。我们还将针对本地化函数$ l $的半左范围与$ L $ - 局部模型结构所谓的合适性相关联。
We extend the group-theoretic notion of conditional flatness for a localization functor to any pointed category, and investigate it in the context of homological categories and of semi-abelian categories. In the presence of functorial fiberwise localization analogous results to those obtained in the category of groups hold, and we provide existence theorems for certain localization functors in specific semi-abelian categories. We prove that a Birkhoff subcategory of an ideal determined category yields a conditionally flat localization, and explain how conditional flatness corresponds to the property of admissibility of an adjunction from the point of view of categorical Galois theory. Under the assumption of fiberwise localization we give a simple criterion to determine when a (normal epi)-reflection is a torsion-free reflection. This is shown to apply in particular to nullification functors in any semi-abelian variety of universal algebras. We also relate semi-left-exactness for a localization functor $L$ with what is called right properness for the $L$-local model structure.
