论文标题
增强的扭曲箭头类别
Enhanced twisted arrow categories
论文作者
论文摘要
给定一个$ \ infty $ -bicateGory $ \ mathbb {d} $，带有基础$ \ infty $ -category $ \ mathcal {d} $，我们构建了一个笛卡尔纤维$ \ operatatorname {tw}（tw}） \ Mathcal {d}^{\ operatoRatorName {op}} $，我们称其为增强的扭曲箭头$ \ infty $ -scategory，对限制的映射类别fuctor进行分类$ \ operatorName {map} _ {\ Mathbb {d}}：\ Mathcal {d}^{\ operatorName {op}} \ times \ times \ times \ times \ mathcal {d} \至\ operatorname {cat} _ {\ infty} $。在这种新结构的帮助下，我们提供了自然转换的$ \ infty $ - 类别$ \ permatatorname {nat}（f，g）$的结局。作为我们结果的应用，我们证明了Arxiv中提出的加权柱的定义：1501.02161满足了预期的二维通用性能。
Given an $\infty$-bicategory $\mathbb{D}$ with underlying $\infty$-category $\mathcal{D}$, we construct a Cartesian fibration $\operatorname{Tw}(\mathbb{D})\to \mathcal{D} \times \mathcal{D}^{\operatorname{op}}$, which we call the enhanced twisted arrow $\infty$-category, classifying the restricted mapping category functor $\operatorname{Map}_{\mathbb{D}}:\mathcal{D}^{\operatorname{op}}\times \mathcal{D} \to \mathbb{D}^{\operatorname{op}} \times \mathbb{D} \to \operatorname{Cat}_{\infty}$. With the aid of this new construction, we provide a description of the $\infty$-category of natural transformations $\operatorname{Nat}(F,G)$ as an end for any functors $F$ and $G$ from an $\infty$-category to an $\infty$-bicategory. As an application of our results, we demonstrate that the definition of weighted colimits presented in arXiv:1501.02161 satisfies the expected 2-dimensional universal property.
