论文标题
左bousfield本地化没有左法
Left Bousfield localization without left properness
论文作者
论文摘要
给定一个组合（半）模型类别$ m $和一组形态$ c $，我们确定了一个半模型类别的存在$ l_c m $，可满足左bousfield本地化的通用属性，在半模型类别类别中。我们的主要工具是杰夫·史密斯（Jeff Smith）结果的半模型分类版本，似乎具有独立的兴趣。我们的主要结果允许定位模型类别，而模型类别无法保持适当。我们提供了许多与Baez-Dolan稳定假设，代数上的代数的定位，色素同拷贝理论，参数化光谱，$ C^*$ - 代数 - 代数，富集类别，DG类别，函数计算器和Voevodsky在raddive fuctors的工作。
Given a combinatorial (semi-)model category $M$ and a set of morphisms $C$, we establish the existence of a semi-model category $L_C M$ satisfying the universal property of the left Bousfield localization in the category of semi-model categories. Our main tool is a semi-model categorical version of a result of Jeff Smith, that appears to be of independent interest. Our main result allows for the localization of model categories that fail to be left proper. We give numerous examples and applications, related to the Baez-Dolan stabilization hypothesis, localizations of algebras over operads, chromatic homotopy theory, parameterized spectra, $C^*$-algebras, enriched categories, dg-categories, functor calculus, and Voevodsky's work on radditive functors.
