johncarlosbaez, 1 month ago

@OscarCunningham - I don't know, but you're reminding me of 𝔸¹ homotopy theory, a blend of algebraic geometry and simpliical homotopy theory pioneered by Voevodsky, where an "edge" (i.e. 1-simplex) is modeled by the affine line 𝔸¹ (corresponding to the ring ℤ[x]), and so on.

I could say more, but I'll point you here:

https://en.wikipedia.org/wiki/A%C2%B9_homotopy_theory

and reading this I'm convinced my answer to your question is not nuts.