In this paper we provide explicit dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and conclude the paper with an explicit dual of the Ne\v{s}et\v{r}il-R\"odl Theorem for relational structures. Instead of embeddings which are crucial for"direct"Ramsey results, for each class of structures under consideration we propose a special class of surjective maps and prove a dual Ramsey theorem in such a setting. In contrast to on-going Ramsey classification projects where the research is focused on fine-tuning the objects, in this paper we advocate the idea that fine-tuning the morphisms is the key to proving dual Ramsey results. Since the setting we are interested in involves both structures and morphisms, all our results are spelled out using the reinterpretation of the (dual) Ramsey property in the language of category theory.

中文翻译：

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关于关系结构的对偶 Ramsey 定理

在本文中，我们为几类有限关系结构（例如有限线性有序图、有限线性有序度量空间和具有线性扩展的有限偏序集）提供了显式对偶 Ramsey 语句，并以 Ne\v 的显式对偶结束本文{s}et\v{r}il-R\"odl Theorem for关系结构。代替对“直接”Ramsey结果至关重要的嵌入，对于所考虑的每一类结构，我们提出了一类特殊的满射映射并证明在这种情况下的对偶拉姆齐定理。与正在进行的拉姆齐分类项目相反，研究重点是微调对象，在本文中，我们主张微调态射是证明对偶拉姆齐的关键的想法结果。由于我们感兴趣的设置涉及结构和态射，我们所有的结果都是使用范畴论语言对（双重）拉姆齐性质的重新解释来说明的。