Symmetric Monoidal Sketches and Categories of Wirings

We introduce a potential application of two-dimensional linear algebra to concurrency. Motivated by the structure of categories of wirings, in particular in action calculi but also in other models of concurrency, we investigate the notion of symmetric monoidal sketch for providing an abstract notion of category of wirings. Every symmetric monoidal sketch generates a generic model. If the sketch is single-sorted, the generic model can be characterised as a free structure on 1, with structure defined coalgebraically. We investigate how these results generalise results about categories of wirings given by Milner and others, and we outline how the constructs may be extended to model controls and dynamics.