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.

You can use Markdown or HTML in your comments. You can also use LaTeX, like this: $latex E = m c^2 $. The word 'latex' comes right after the first dollar sign, with a space after it.

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.