Today involved enjoyable meetings-up at coffee tree roasters and later meatloafings-up with
I had some interesting further thoughts about formulating a certain kind of higher-dimensional graph based on an intuition that a pasting diagram of n-cells looks a lot like an n-sphere missing one cell. That is, you can express the (n-1)-dimensional domain and codomain of such an "n-path" by an extra cell that "wraps around" the composition into a cycle so that now every (n-1)-cell has exactly one n-cell to whose domain it belongs, and exactly one n-cell to whose codomain it belongs. While spacing out at the 7 party last night I thought I had discovered a fatal flaw in this plan, but now I think I see how to work around it.