String Diagrammatic Electrical Circuit Theory

Guillaume Boisseau
(University of Oxford, UK)
Paweł Sobociński
(Tallinn University of Technology, Estonia)

We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements, and the impedance calculus, a powerful toolbox for diagrammatic reasoning on circuit diagrams. We demonstrate the power of our approach by giving idiomatic proofs of several textbook results, including the superposition theorem and Thevenin's theorem.

In Kohei Kishida: Proceedings of the Fourth International Conference on Applied Category Theory (ACT 2021), Cambridge, United Kingdom, 12-16th July 2021, Electronic Proceedings in Theoretical Computer Science 372, pp. 178–191.
Published: 3rd November 2022.

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