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.

中文翻译：

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范畴论视角下的 Kechris-Pestov-Todorčević 通信

Kechris-Pestov-Todorčević 对应关系（简称 KPT 对应关系）是模型理论、组合学和拓扑动力学之间令人惊讶的对应关系。在本文中，我们提出了对（部分）KPT 对应关系的分类重新解释，目的是证明双重陈述。我们的策略是采用“直接”结果，然后通过提供结果的分类版本的纯粹分类证明来分析使结果真实的必要基础设施。然后我们可以利用对偶原理几乎免费获得对偶语句。我们相信 KPT 对应的双重版本不仅可以提供对这种对应结合在一起的组合、模型理论和拓扑现象的相互作用的新见解，