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.

翻译：我们将强profunctor的态射识别为量子超映射的范畴化。这些带洞图的黑盒推广因此被置于更广泛的profunctor光学领域中，作为具体网络上共预层范畴中的态射。这首次实现了在完全理论无关的设定下为超映射构建抽象逻辑连接词（如张量积与否定）。研究发现，这些逻辑连接词足以抽象建模量子超映射理论的关键结构特征：黑盒不定因果序、黑盒确定因果序，以及确定因果序超映射分解为具体电路图。我们证明这些分解定理的核心在于米田引理与可表示性概念。