M Theory Lesson 77
Now Ross Street has published a book, Quantum Groups: a Path to Current Algebra, which I would love to get my hands on. The book blurb says, "A key to understanding these new developments is categorical duality." That simply means the duality given by turning a tree upside down, as drawn, so we need operad structures that combine upward branches and downward branches. Leaping ahead to triality, one expects branchings in three directions and no chosen root. Such diagrams are associated to cyclic operads, and we actually consider these with polygonal tilings, since the dual to a polygon is a branching tree with no real root.