标题： 关系的 Dagger 范畴：拖延 Dagger 范畴与满射正则独立范畴的等价性 显示英文标题

标题： Dagger categories of relations: the equivalence of dilatory dagger categories and epi-regular independence categories

摘要： 几个类别看起来像关系的类别，但不符合正则范畴中已建立的关系理论。 它们包括满射多值函数的类别、单射部分函数的类别、有限概率空间和随机矩阵的类别，以及希尔伯特空间和线性压缩的类别。 为了解释这些异常例子，我们发展了在满射正则独立范畴中的关系并行理论。 正如正则范畴对应于可表的双有理范畴，满射正则独立范畴对应于拖延的自伴范畴。 这种等价将满射正则独立范畴映射到其相关的自伴关系范畴，并将拖延的自伴范畴映射到其共等距的宽子范畴。 显示英文摘要

摘要： Several categories look like categories of relations, but do not fit the established theory of relations in regular categories. They include the category of surjective multivalued functions, the category of injective partial functions, the category of finite probability spaces and stochastic matrices, and the category of Hilbert spaces and linear contractions. To explain these anomalous examples, we develop a parallel theory of relations in epi-regular independence categories. Just as regular categories correspond to tabular allegories, epi-regular independence categories correspond to dilatory dagger categories. The equivalence maps epi-regular independence categories to their associated dagger category of relations, and dilatory dagger categories to their wide subcategory of coisometries.