We observe that the existence of sequential and parallel composition supermaps in higher order physics can be formalised using enriched category theory. Encouraged by physically relevant examples such as unitary supermaps and layers within higher order causal categories (HOCCs), we treat the modelling of higher order physical theories with enriched monoidal categories in analogy with the modelling of physical theories are with monoidal categories. We use the enriched monoidal setting to construct a suitable definition of structure preserving map between higher order physical theories via the Grothendieck construction. We then show that the convenient feature of currying in higher order physical theories can be seen as a consequence of combining the primitive assumption of the existence of parallel and sequential composition supermaps with an additional feature of linking. In a second application we use our definition of structure preserving map to show that categories containing infinite towers of enriched monoidal categories with full and faithful structure preserving maps between them inevitably lead to closed monoidal structures. The aim of the proposed definitions is to step towards providing a broad framework for the study and comparison of novel causal structures in quantum theory, and, more broadly, a paradigm of physical theory where static and dynamical features are treated in a unified way.

翻译：我们观察到,在较高等级物理学中,有顺序和平行构成的超级图的存在可以通过浓缩类别理论正式化。在诸如单一超级图和高等级因果类别(HOCCs)中的层次等具有物理相关性的例子的鼓励下,我们把较高等级物理理论的模型化与浓缩的单亚相类类比较,与物理理论的模型化比较。我们利用浓缩的单亚相系设置来构建一个适当的结构定义,通过格罗特菲克的构造来保护较高等级物理理论之间的结构。然后我们表明,在较高等级物理理论中,曲线化的方便特征可以被看成是将平行和顺序构成的原始假设与另一个关联特征相结合的结果。在第二个应用中,我们使用我们对结构保护地图的定义来显示,含有富集的单亚相系的无穷塔的完整和忠实结构保存地图的类别必然导致封闭的单一结构。拟议定义的目的是为研究与比较量子理论中新的因果结构提供一个广泛的框架,以及更广义的物理理论范例,以统一的方式处理静态和动态特征。