Morphisms for resistive electrical networks

This paper presents a notion of morphism for resistive electrical networks. One can regard symmetries of a resistive network as morphisms, but they are trivial in the sense that they do not reduce the size of the problem. However, symmetries do induce a nontrivial quotient. We extend this result to arbitrary morphisms in a suitable categorical framework. Our principal application is to solve Kirchoff’s problem for certain products of paths.