论文标题
$（\ infty，2）$ - 类别的纤维和宽松限制
Fibrations and lax limits of $(\infty,2)$-categories
论文作者
论文摘要
我们研究了给定的基本$ \ Mathcal {B} $的四种类型的（CO）$ \ infty $ -BICATEGOIRE，并证明它们编码了$ \ Mathcal {B} $的四个方差风味 - $ \ suftty $ cagiores的索引图。然后，我们使用此机械来设置一个有价值的图表的2（CO）限制的通用理论，该图表$ \ infty $ - 贝格戈里（BigateGory），能够表达lax，加权和伪限制。当手头的$ \ infty $ -BICATEGORY是由对标记的简单组进行张紧的模型类别引起的，我们表明，2-（co）限制的概念可以作为对模型分类级别的加权同置限制的合适形式进行计算，因此在这些2-（CO）限制中尤其显示了这些示例范围的范围内的限制。我们通过讨论适合此设置的辅助性的概念来结束，并使用它来推断出一旦存在的2-（CO）限制的独立性。
We study four types of (co)cartesian fibrations of $\infty$-bicategories over a given base $\mathcal{B}$, and prove that they encode the four variance flavors of $\mathcal{B}$-indexed diagrams of $\infty$-categories. We then use this machinery to set up a general theory of 2-(co)limits for diagrams valued in an $\infty$-bicategory, capable of expressing lax, weighted and pseudo limits. When the $\infty$-bicategory at hand arises from a model category tensored over marked simplicial sets, we show that this notion of 2-(co)limit can be calculated as a suitable form of a weighted homotopy limit on the model categorical level, thus showing in particular the existence of these 2-(co)limits in a wide range of examples. We finish by discussing a notion of cofinality appropriate to this setting and use it to deduce the unicity of 2-(co)limits, once exist.
