论文标题
从类别理论的角度来看，Kechris-Pestov-todor \Vcević的信函
The Kechris-Pestov-Todor\vcević correspondence from the point of view of category theory
论文作者
论文摘要
Kechris-Pestov-Todorčević的对应（简称KPT对应）是模型理论，组合学和拓扑动力学之间的惊人对应关系。在本文中，我们提出了对KPT对应的（一部分）的分类重新解释，目的是证明双重语句。我们的策略是取得“直接”结果，然后分析必要的基础架构，从而通过提供结果的分类版本提供纯粹的分类证明，从而使结果成立。然后，我们可以利用二元性原则，几乎可以免费获得双重陈述。我们认为，KPT对应的双重版本不仅可以为组合，模型理论和拓扑现象的相互作用提供新的见解，而且还可以探索组合现象的分类治疗方法可以接受我们。
The Kechris-Pestov-Todorčević correspondence (KPT-correspondence for short) is a surprising correspondence between model theory, combinatorics and topological dynamics. In this paper we present a categorical re-interpretation of (a part of) the KPT-correspondence with the aim of proving a dual statement. Our strategy is to take a "direct" result and then analyze the necessary infrastructure that makes the result true by providing a purely categorical proof of the categorical version of the result. We can then capitalize on the Duality Principle to obtain the dual statements almost for free. We believe that the dual version of the KPT-correspondence can not only provide the new insights into the interplay of combinatorial, model-theoretic and topological phenomena this correspondence binds together, but also explores the limits to which categorical treatment of combinatorial phenomena can take us.
