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：我们引入标称字符串图，将其定义为标称集合范畴内的内蕴字符串图。由此提出标称PROP与标称幺半理论的概念。研究表明，普通PROP范畴与标称PROP范畴之间存在等价关系。该等价性进一步拓展至对称幺半理论与标称幺半理论，从而使得字符串图的普通演算与标称演算之间的完备性结论得以迁移。