物理学、拓扑学、逻辑学和计算：罗塞塔石碑
Physics, Topology, Logic and Computation: A Rosetta Stone
摘要：
在物理学中，费曼图被用来推理量子过程。在20世纪80年代，人们清楚地认识到，这些图的基础是量子物理学和拓扑学之间的一个强有力的类比：即，线性算子的行为非常像“配边”。类似的图可以用来推理逻辑，它们代表证明，和计算，它们代表程序。随着人们对量子密码学和量子计算的兴趣的增加，很明显，在物理学、拓扑学、逻辑学和计算之间存在着广泛的类比网络。在本文中，我们利用“闭对称monoidal范畴”的概念使其中的一些类比更为精确。我们假设没有范畴论，证明论或计算机科学的先验知识。
英文摘要：
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.
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