The universal simplicial bundle is a simplicial group
arXiv:1204.4886
Abstract
The classical universal bundle functor W:sGrp(C) \to sSet(C) for simplicial groups in a category C with finite products lifts to a monad on sGrp(C). This result extends to simplicial algebras for any Lawvere theory containing that of groups.
5 pages. Main result dates from 2007. Original submission was titled 'W is a monad'. Updated July 2012 to include comments about simplicial monoids