Categories: the Mathematics of Connection

I gave this talk at Mathematics of Collective Intelligence, a workshop organized by Jacob Foster at UCLA’s Institute of Pure and Applied Mathematics, or IPAM for short. There have been a lot of great talks here, all available online.

Perhaps the main interesting thing about this talk is that I sketch some work happening at the Topos Institute where we are using techniques from category theory to design epidemiological models:

Categories: the mathematics of connection

Abstract. As we move from the paradigm of modeling one single self-contained system at a time to modeling ‘open systems’ which interact with their — perhaps unmodeled — environment, category theory becomes a useful tool. It gives a mathematical language to describe the interface between an open system and its environment, the process of composing open systems along their interfaces, and how the behavior of a composite system relates to the behaviors of its parts. It is far from a silver bullet: at present, every successful application of category theory to open systems takes hard work. But I believe we are starting to see real progress.

You can see my slides or watch a video of my talk on the IPAM website or here:

For some other related talks, see:

Monoidal categories of networks.

Symmmetric monoidal categories: a Rosetta stone.

To read more about my work on categories and open systems, go here:

Network theory.

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