I learned about something really cool yesterday and now I feel the need to share it.

I learned about a really new field of math called Discrete Homotopy Theory. This is a homotopy theory for simple graphs that seems different than the classical homotopy theory of graphs thought of as CW complexes. Fascinatingly, there turn out to be two “exotic” homotopy theories for undirected graphs. One of them is called $\times$-homotopy theory, which this paper gives a nice introduction to. The other, which I’m going to focus on in this post, is called discerete homotopy theory or A-homotopy theory[^1]

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