The Category of Kirchhoff Relations

Abstract

We define the category of Kirchhoff relations to consist of those Lagrangian relations that conserve total momentum – a condition that can also be interpreted as Kirchhoff’s current law. We study and characterize different subcategories of Kirchhoff relations and present universal sets of generators of the different subcategories of Kirchhoff relations. These generators can be interpreted as junctions of ideal wires, resistances, voltage sources and current sources