Relational structures are emerging as ubiquitous mathematical machinery in the semantics of open systems of various kinds. Cartesian bicategories are a well-known categorical algebra of relations that has proved especially useful in recent applications. The passage between a category and its bicategory of relations is an important question that has been widely studied for decades. We study an alternative construction that yields a cartesian bicategory of relations. Its behaviour is closely related to the axiom of choice, which itself can be expressed in the language of cartesian bicategories.

中文翻译：

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有选择的笛卡尔双分类

关系结构正在成为各种开放系统语义中无处不在的数学机制。笛卡尔二分类是众所周知的关系分类代数，在最近的应用中被证明特别有用。范畴与其双范畴关系之间的过渡是几十年来被广泛研究的一个重要问题。我们研究了一种替代构造，它产生了笛卡尔关系的双分类。它的行为与选择公理密切相关，选择公理本身可以用笛卡尔双范畴的语言来表达。