The challenge of global warming brings into clear view the need for improved integration between category theory and other fields. Among other things, we need categories to understand networks. To describe systems composed of interacting parts, scientists and engineers draw diagrams of networks: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams and the like. All these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. Two complementary approaches are presentations of props using generators and relations (which are more algebraic in flavor) and decorated cospan categories (which are more geometrical). In this talk we focus on the former.
You can see the slides here and watch a video here.
This talk assumes considerable familiarity with category theory. For a much gentler talk on the same theme, see:
To read more about the network theory project, go here: