• John Baez and Brendan Fong, A compositional framework for passive linear networks, *Theory and Applications of Categories* **33** (2018), 1158–1222.

The referee took a long time, but they caught some serious errors and also demanded a major restructuring of the paper. We rewrote it using Brendan’s ideas on decorated corelations, and it’s become a much deeper paper, but also shorter.

Brendan is coming by this Sunday—Thanksgiving weekend—and we’ll celebrate the end of a project that started in 2013.

]]>• John Baez, Brandon Coya and Franciscus Rebro, Props in network theory.

We illustrate the usefulness of props by giving a new, shorter proof of the ‘black-boxing theorem’ proved here:

• John Baez and Brendan Fong, A compositional framework for passive linear networks. (Blog article here.)

]]>• Jonathan Lorand and Fabrizio Genovese, Hypergraph categories of cospans, The *n*-Category Café, 28 February 2018.

What’s especially interesting to me is that both Jonathan and Fabrizio know some mathematical physics, and they’re part of a group who will be working with me on some problems as part of the Applied Category Theory 2018 school! Brendan and Blake Pollard and I used symplectic geometry and decorated cospans to study the black-boxing of electrical circuits and Markov processes… maybe we should try to go further with that project!

]]>• John Baez and Brendan Fong, A compositional framework for

passive linear networks. (Blog article here.)

or my paper with Blake Pollard on reaction networks:

• John Baez and Blake Pollard, A compositional framework for reaction networks.

will find many of Darbo’s ideas eerily similar.

]]>Brendan was the first to join the project. I wanted him to work on electrical circuits, which are a nice familiar kind of network, a good starting point. But he went much deeper: he developed a general category-theoretic framework for studying networks. We then applied it to electrical circuits, and other things as well.

]]>Brendan was the first to join the project. I wanted him to work on electrical circuits, which are a nice familiar kind of network, a good starting point. But he went much deeper: he developed a general category-theoretic framework for studying networks. We then applied it to electrical circuits, and other things as well.

]]>• John Baez and Brendan Fong, A compositional framework for passive linear circuits. (Blog article here.)

The key point is simply that you use conductive wires to connect resistors, inductors, capacitors, batteries and the like and build interesting circuits—so if you don’t fully understand the math of conductive wires, you’re limited in your ability to understand circuits in general!

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