We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the definable categories. The syntax of our relational algebraic theories is string-diagrammatic, and can be seen as an extension of the usual term syntax for algebraic theories.

中文翻译：

---

关系型通用代数的变分定理

我们开发了通用代数的类似物，其中生成符号被解释为关系。我们证明了这些关系代数理论的一个多样性定理，其中我们发现它们的模型类别恰好是可定义的类别。我们的关系代数理论的语法是字符串语法的，可以看作是代数理论的常用术语语法的扩展。