Since there are digital manifolds, then are there / why aren't there topologies for electronics?
Since I was imagining that even though the display of a computer is mathematically "simpler" since it bases on a 2D Euclidean grid, then since many electronics are basically just some sort of functions operating on some (possibly functional) spaces, then does there exist "complete" (i.e. something that describes an "entirety" of a circuit) mathematical formalisms for electronics logic?
Or perhaps there does exist, but since I'm not that trained in electronics engineering, I cannot identify those formalisms. I'd expect that e.g. the "black box abstraction" is this sort of thing, just that I don't know if it "transfers" formalisms outside of boxes or whether all boxes are somehow "independent" structures.
A couple of category-theoretic approaches have recently been mentioned on the n-Category Café blog:
Props in network theory
Circuits, Bond Graphs, and Signal-Flow Diagrams