The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern presentation of these ``categories for relations'', including their enriched version, further showing how they arise as Kleisli categories of symmetric monoidal monads. The resulting taxonomy aims at bringing clarity and organisation to the many related concepts and frameworks occurring in the literature.

翻译：关于抽象关系结构属性的范畴研究多年来已得到广泛发展，形成了丰富多样的研究成果。本文旨在提供这些"关系范畴"的现代呈现，包括其丰富化版本，并进一步展示它们如何作为对称幺半单子的克莱斯利范畴出现。由此产生的分类法旨在为文献中出现的众多相关概念与框架带来清晰性与系统性。