Given a comonad on a category , a natural transformation is a symmetry of if it sastisfies the quantum Yang-Baxter equation (transposed braid relation)
In that case, the pair is called a symmetric comonad.
The simplicial set obtained by the standard construction from a symmetric comonad has always a structure of a symmetric simplicial set.
M. Grandis, Finite sets and symmetric simplicial sets, Theory of Applications of Categories, Vol. 8, No. 8, pp. 244–253, link (to come?).
Z. Škoda, Cyclic structures for simplicial objects from comonads, math.CT/0412001.
Revised on December 18, 2009 03:15:15
by Toby Bartels