We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order bipartite processes and higher-order bipartite states. In category-theoretic terms, these laws are expressed using enrichment and cotensors in symmetric polycategories, along with a frobenius-like coherence between them. We describe how these laws capture the salient features of higher-order quantum theory, and discover an upper bound for higher-order circuits: any higher-order circuit theory embeds into the theory of strong profunctors.

翻译：我们为（严格）高阶电路图建立了一系列基本定律。具体而言，我们通过以下三个方面定义高阶电路理论：（a）嵌套，（b）时间与空间组合，以及（c）低阶二分过程与高阶二分态之间的等价性。在范畴论术语中，这些定律利用对称多范畴中的充实与余张量，以及它们之间类似Frobenius结构的协调性来表达。我们阐述了这些定律如何捕捉高阶量子理论的显著特征，并发现了高阶电路的一个上界：任何高阶电路理论均可嵌入到强profunctor理论中。