AI 中文总结
本文在∞-范畴框架下，通过相对Rezk nerve的Mazel-Gee公式，将Dwyer–Kan的吊床局部化描述为Segal anima，计算其映射anima并推广原公式，为相关文献公式提供统一处理。
AI 中文摘要
我们在∞-范畴的框架下，对Dwyer–Kan的吊床局部化给出了简短且概念性的阐述。从Mazel-Gee通过相对Rezk nerve实现局部化的公式出发，我们证明其Segal化可明确描述为之字形的Segal anima。我们还计算了其映射anima，并还原且推广了Dwyer–Kan的吊床公式。作为应用，我们证明当相对∞-范畴支持分式时，局部化的映射anima可获得简洁描述，这为现有文献中若干此类公式提供了统一处理方式。
英文摘要
We give a short, conceptual account of Dwyer--Kan's hammock localization in the setting of $\infty$-categories. Starting from Mazel-Gee's formula for localization via the relative Rezk nerve, we show that its Segalification can be described explicitly as a Segal anima of zig-zags. We also compute its mapping animae and recover and generalize Dwyer--Kan's hammock formula. As an application, we show that, when a relative $\infty$-category supports fractions, the mapping animae of localization admit a simple description. This gives a unifying treatment for several formulas of this type in the existing literature.
Comments41 pages, comments welcome!
