A canonical enriched Adams–Hilton model for simplicial sets

For any 1-reduced simplicial set K we define a canonical, coassociative coproduct on ΩC(K), the cobar construction applied to the normalized, integral chains on K, such that any canonical quasi-isomorphism of chain algebras from ΩC(K) to the normalized, integral chains on GK, the loop group of K, is a coalgebra map up to strong homotopy. Our proof relies on the operadic description of the category of chain coalgebras and of strongly homotopy coalgebra maps given in [K. Hess, P.-E. Parent, J. Scott, Bimodules over operads characterize morphisms, preprint, math.AT/0505559, 2005].