SSetElement

A simplex of a finitely-generated simplicial set, in Eilenberg–Zilber normal form: word is the strictly decreasing list of degeneracy indices [w1 > w2 > ... > wk] such that this element is s_w1 s_w2 ... s_wk (generator), read outermost-first (s_w1 is the last degeneracy applied). word = Nil means the element is generator, which must be non-degenerate. Dimension is generator's own dimension plus word.length.

Decreasing, not increasing: s_i s_j = s_{j+1} s_i for i <= j takes a non-decreasing adjacent pair to a decreasing one, e.g. s_0 s_0 = s_1 s_0 -- so the (unique) normal form for "apply s_0 twice" is [1, 0], never [0, 1].