一句话：用强 profunctor 的态射将量子超映射范畴化，并给出理论无关的抽象逻辑连接词与分解定理。
本文为量子超映射（supermap）建立 profunctor 语义。作者将强 profunctor 的态射视为量子超映射的范畴化，把这类带洞图的黑箱推广置于 profunctor optics 框架中，即具体网络上的余预层范畴的态射。该视角首次在完全理论无关的设定下构造超映射的张量积、否定等抽象逻辑连接词。作者表明，这些连接词足以抽象建模量子超映射理论的关键结构特征：黑箱不定因果序、黑箱确定因果序，以及确定因果序超映射到具体线路图的分解。进一步展示这些分解定理的核心是 Yoneda 引理与可表示性概念。
We identify morphisms of strong profunctors as a categorification of quantum supermaps. These black-box generalisations of diagrams-with-holes are hence placed within the broader field of profunctor optics, as morphisms in the category of copresheaves on concrete networks. This enables the first construction of abstract logical connectives such as tensor products and negations for supermaps in a totally theory-independent setting. These logical connectives are found to be all that is needed to abstractly model the key structural features of the quantum theory of supermaps: black-box indefinite causal order, black-box definite causal order, and the factorisation of definitely causally ordered supermaps into concrete circuit diagrams. We demonstrate that at the heart of these factorisation theorems lies the Yoneda lemma and the notion of representability.