https://en.wikipedia.org/wiki/Simplex_category Thinnings are also the morphisms in the simplex category. Simplicial sets are a way of organizing face-edge that use this category as an indexing structure. Is it surprising that de Bruijn manipulations and describing shapes could share this structure? Maybe. Simplicial sets add in degenerate triangles (like a triangle with only 2 distinct vertices (kind of a “thick” line) or even only 1 distinct vertex (a “thick” point)). These are added in because it makes things cleaner. This degenerayc and tossing stuff away does kind of jive with thinning. Nameless Projections kind of jive with thinning. I dunno. If a triangle is a list of 3 points, the oriented edges are kind of the 2 vertex sublists of that and the vertices are kind of the 1 vertex sublists.
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