  We give a short and streamlined proof of the following statement recently
proven by the author and M. Zeinalian: the cobar construction of the dg
coassociative coalgebra of normalized singular chains on a path-connected
pointed space is naturally quasi-isomorphic as a dg associative algebra to the
singular chains on the based loop space. This extends a classical theorem of F.
Adams originally proven for simply connected spaces. Our proof is based on
relating the cobar functor to the left adjoint of the homotopy coherent nerve
functor.
