The Topos Institute is in business! I’m really excited about visiting there this summer and working on applied category theory.
They recently had a meeting with some people concerned about AI risks, called Finding the Right Abstractions, organized by Scott Garrabrant, David Spivak, and Andrew Critch. I gave a gentle introduction to the uses of symmetric monoidal categories:
• Symmetric monoidal categories: a Rosetta Stone.
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. While originally the morphisms in such categories were mainly used to describe processes, we can also use them to describe open systems.
You can see the slides here, and watch a video here:
For a lot more detail on these ideas, see:
• John Baez and Mike Stay, Physics, topology, logic and computation: a Rosetta Stone, in New Structures for Physics, ed. Bob Coecke, Lecture Notes in Physics vol. 813, Springer, Berlin, 2011, pp. 95—174.