A chain coalgebra model for the James map

Abstract

Let EK be the simplicial suspension of a pointed simplicial set K. We construct a chain model of the James map, K : CK CEK. We compute the cobar diagonal on CEK, not assuming that EK is 1-reduced, and show that K is comultiplicative. As a result, the natural isomorphism of chain algebras T CK = CK preserves diagonals.