Codescent Theory I：Foundations（英语：Codescent Theory I：Foundations）
Codescent theory I: Foundations
摘要：
考虑共纤生成的模型类别$S$、小范畴$C$和$C$的子类别$D$。我们赋予从$C$到$S$的函子范畴$S^C$一个模型结构，定义弱等价和纤维化，但只在$D$上。我们首先关注的是移动$C$、$D$和$S$的影响。这里介绍的主要概念是$S^C$中对象的“$D$ -codescent”属性。我们的长期计划旨在将鲍姆-康纳斯和法雷尔-琼斯的猜想重新表述为代码陈述，并用新的方法解决它们。在这里，我们建立了一个系统的代码下降理论的基础，包括拉回，推进和各种不变性。
英文摘要：
Consider a cofibrantly generated model category $S$, a small category $C$ and a subcategory $D$ of $C$. We endow the category $S^C$ of functors from $C$ to $S$ with a model structure, defining weak equivalences and fibrations objectwise but only on $D$. Our first concern is the effect of moving $C$, $D$ and $S$. The main notion introduced here is the ``$D$-codescent'' property for objects in $S^C$. Our long-term program aims at reformulating as codescent statements the Conjectures of Baum-Connes and Farrell-Jones, and at tackling them with new methods. Here, we set the grounds of a systematic theory of codescent, including pull-backs, push-forwards and various invariance properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
