Re: only_marketing_?

[John Baez <baez@math.ucr.edu>]

Hi -

Steve wrote:

> So, to return to John Baez's interview, how might we look for category
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


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