To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, electrical circuit diagrams, signal-flow graphs, Feynman diagrams and the like. In principle all these different diagrams fit into a common framework: the mathematics of monoidal categories. This has been known for some time. However, the details are more challenging, and ultimately more rewarding, than this basic insight. Here we explain how various applications of reaction networks and Petri nets fit into this framework.
You can see the slides here.
There are lots of links to papers in the slides, especially near the end. To read more about the network theory project, go here:
For a video of a related talk assuming more knowledge of category theory, try this: