My interest in Howard Odum's work is part of why I put a lot of work into formulating electrical circuit theory in terms of categories. Electrical circuits are just one of many kinds of networks for which a rigorous set of analogies exist, and category theory can handle all these networks!

I wrote about these analogies in my blog series on network theory:

* Part 27 - Getting differential equations from circuit diagrams. Available on Azimuth.

* Part 28 - The analogy between electronics and mechanics. Available on Azimuth.

* Part 29 - Analogies between the mechanics of translation, the mechanics of rotation, electronics, hydraulics, thermal physics, chemistry, heat flow and economics. Flow versus effort. Available
on Azimuth.

Then Brendan Fong, who was my student at the time, added the category theory! His thesis is a great place to start:

* Brendan Fong, The Algebra of Open and Interconnected Systems, Ph.D. thesis, University of Oxford, 2016. (Blog article here.)

We've subsequently developed this further:

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

It took us many years to finish this paper!