So, to return to John Baez's interview, how might we look for category
Hi - Steve wrote: theory
helping to understand the world's problems? We must first look for objects and morphisms,with identities and associative composition, so what are the real-world prototypes of what we are trying to do there? What is the first step beyond the vague aspirations?
The interviewer didn't give me a chance to say much. Personally I've been trying to understand the various kind of "networks" that come up in electrical engineering: https://arxiv.org/abs/1504.05625 control theory: https://arxiv.org/abs/1405.6881 chemistry: https://arxiv.org/abs/1704.02051 and the study of Markov processes: https://arxiv.org/abs/1508.06448 Researchers in these and many other subjects use diagrams to describe the networks they're working with. These diagrams are morphisms in various symmetric monoidal categories. So there are already plenty of symmetric monoidal categories being put to work in applied math. But which ones, exactly? That's what my papers are about. These categories turn out to be beautiful and not always familiar; trying to understand them is making my students and me come up with new ideas. So, right now, I'd say researchers in these subjects have more to teach category theorists than vice versa. Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]