一句话：系统梳理抽象关系结构性质的各类范畴，并揭示其作为对称幺半单子 Kleisli 范畴的统一来源。
关系可以承载丰富的结构性质，而对这类结构进行范畴抽象的“关系范畴”研究已积累大量但分散的成果。本文旨在给出一份现代风格的统一呈现，系统整理这些关系范畴，并进一步讨论其丰富化（enriched）版本。作者展示这些范畴如何作为对称幺半单子（symmetric monoidal monad）的 Kleisli 范畴出现，从而在单子与关系结构之间建立联系。由此得到的分类体系（taxonomy）用于澄清并组织文献中众多相关概念与框架，帮助读者理解不同构造之间的层次与关联。论文属于范畴论/语义学方向的理论工作，主要贡献是概念梳理与统一视角。
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.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{abs-2502-10323,
title = {A taxonomy of categories for relations},
author = {Cipriano Junior Cioffo and Fabio Gadducci and Davide Trotta},
journal = {Logical Methods in Computer Science},
volume = {Volume 22, Issue 2},
year = {2026},
doi = {10.46298/lmcs-22(2:36)2026}
}