There is an obvious notion of composition for electrical circuits: just solder some terminals together. But what how do we compute the behaviour of the composite system from an understanding of its parts, and exactly what algebraic structure is present? Viewing a passive linear circuit as an object that constrains the current- potential readings at its terminals to lie in a specific linear subspace, in this talk we will discuss how to construct a monoidal functor from a category of circuit diagrams to the category of linear relations that expresses this semantics. This represents the beginning of a categorical account of Willems´ behavioural approach to open and interconnected systems.

This is joint work with John Baez.