Recorded 16 February 2022. John Baez of University of California, Riverside, Mathematics presents "Categories: the Mathematics of Connection" at IPAM's Mathematics of Collective Intelligence Workshop. 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.