Thanks, everyone! I urge you all to continue reading beyond Chapter 4.
Chapter 5 is about signal flow graphs in control theory, and "props", which are certain nice monoidal categories. My students Jason and Brandon wrote their theses on these topics:
* Jason Erbele, Categories in
Control: Applied PROPs
, Ph.D. thesis, U. C. Riverside, 2016.
* Brandon Coya, Circuits,
Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective
Ph.D. thesis, U. C. Riverside, 2018. (Blog article
and Brendan has worked on these too, and so have I:
* Brandon Coya and Brendan Fong,
"https://arxiv.org/abs/1601.02307">Corelations are the
prop for extraspecial commutative Frobenius monoids,
Theory and Applications of Categories 32
380–395. (Blog article
* John Baez, Brandon Coya and Franciscus Rebro,
"https://arxiv.org/abs/1707.08321">Props in network theory,
Theory and Applications of Categories 33
(Blog article here
so this material is almost painfully familiar to me.
Chapter 6 is on circuit diagrams, and both Brandon and Brendan did their theses with me on this topic. Brandon Coya's thesis is above, and Brendan's is here:
* Brendan Fong, The Algebra
of Open and Interconnected Systems
, Ph.D. thesis, University of
Oxford, 2016. (Blog article here
based in part on this paper, which is still fighting its way through the referees:
* John Baez and Brendan Fong,
"https://arxiv.org/abs/1504.05625">A compositional framework for
passive linear networks. (Blog article
Chapter 7 is on topos theory, which is very different, but also fascinating.