We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are equivalent. This equivalence is then extended to symmetric monoidal theories and nominal monoidal theories, which allows us to transfer completeness results between ordinary and nominal calculi for string diagrams.
翻译:我们引入了名义字符串图, 在名义数据集类别中作为字符串图内部。 这导致我们定义了名义 PROP 和名义 单向理论。 我们显示普通 PROP 和名义 PROP 的类别是等效的。 然后这一等值扩展至对称的单向理论和名义 单向理论, 这使得我们可以在普通的和名义的字符串图计算之间转换完整性结果 。