tag:blogger.com,1999:blog-7307840825023135484.post6613152809778971168..comments2023-04-16T03:44:23.949+12:00Comments on Arcadian Pseudofunctor: Knotty Gauge Theory IIIKeahttp://www.blogger.com/profile/05652514294703722285noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7307840825023135484.post-10680798434357941662011-04-15T19:31:46.829+12:002011-04-15T19:31:46.829+12:00OK, so any Lie algebra (for instance) has a secret...OK, so <i>any</i> Lie algebra (for instance) has a secret ternary structure, because of the Jacobi identity. We are always thinking in abstract terms: pre algebras, pre spacetimes. The cyclicity number $p$ is many things, such as the cardinality of the Fun Set, where Fun is that old <i>field with one element</i>, or dimension of MUB space, or ... <br /><br />One day some years ago (around 2006) I was sitting in a pub by Michael Batanin, and he was musing about cyclic generalisations of categorical sources and targets, somewhat along these motivic lines ... at the time, my ears pricked up, because I knew it somehow had to be the same thing that us dumb physicists were after, but it is taking a while for it to be worked out ...Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.comtag:blogger.com,1999:blog-7307840825023135484.post-21322283471620740122011-04-15T19:14:12.953+12:002011-04-15T19:14:12.953+12:00Long term readers will recall the aim to use highe...Long term readers will recall the aim to use higher dimensional category theory (via physical motives and Batanin's polytopes) to generalise the case of the associahedra planar rooted trees. The associahedra are used to tile the (real points of the) moduli spaces for Riemann surfaces with $n$ marked points. Here we start to see 'cyclic trees', where we get $p$ copies of something where $p = 3$ will show up a lot in association with color and generation. See comments in the next post.Keahttps://www.blogger.com/profile/05652514294703722285noreply@blogger.com