22 June 2017:
Here is this week's progress, as far as I know:
1) I'm visiting the University of Genoa. It's home to 3 well-known category theorists:
* Marco Grandis (who works on double and n-tuple categories),
* Giuseppe Rosolini (who does functorial semantics for programming languages) and
* Eugenio Moggi (the guy who introduced monads in computer science - a big deal in Haskell and some other languages).
Marco Grandis told me something very interesting. His advisor, Gabriele Darbo, introduced a "theory of devices" in 1970, based on the category of corelations! He applied it to linear electrical circuits using the "add currents, duplicate voltages" rule. All this is VERY similar to Brendan's thesis work and also some of my work with Blake. But it's also different!
Yesterday I summarized the ideas here:
* [The theory of devices](https://johncarlosbaez.wordpress.com/2017/06/20/the-theory-of-devices/).
I haven't had time yet to think hard about how his formalism connects to ours. Darbo's work was mostly ignored, perhaps because it's all in Italian. I think we can still learn something from it, even though we've gone further.
2) Today I gave a general talk for the math and science faculty here at Genoa:
* [Tales of the dodecahedron: from Pythagoras to Plato to Poincaré](http://math.ucr.edu/home/baez/dodecahedron/genoa_talk/1.html).
3) I also gave a talk to the math department:
* [Applied category theory](http://math.ucr.edu/home/baez/control/applied_category_theory.pdf).