Here are the slides of my talk at the workshop on compositionality at the Simons Institute for the Theory of Computing next week. I decided to talk about some new work with Blake Pollard. You can see slides here:
• John Baez, Compositionality in network theory, 6 December 2016.
and a video here:
Abstract. 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. In principle all these different diagrams fit into a common framework: the mathematics of symmetric monoidal categories. This has been known for some time. However, the details are more challenging, and ultimately more rewarding, than this basic insight. Two complementary approaches are presentations of symmetric monoidal categories 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 latter.
This talk assumes considerable familiarity with category theory. For a much gentler talk on the same theme, see: