A canonical enriched Adams-Hilton model for simplicial sets

Abstract

For any 1-reduced simplicial set $K$ we define a canonical, coassociative coproduct on $\Om C(K)$, the cobar construction applied to the normalized, integral chains on $K$, such that any canonical quasi-isomorphism of chain algebras from $\Om C(K)$ 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 math.AT/0505559.

Theorems & Definitions (32)

• definition 1
• definition 2
• definition 3
• definition 4
• proof
• definition 5
• definition 6
• proof
• definition 7
• proof