  The loop product is an operation in string topology. Cohen and Jones gave a
homotopy theoretic realization of the loop product as a classical ring spectrum
$LM^{-TM}$ for a manifold $M$. Using this, they presented a proof of the
statement that the loop product is isomorphic to the Gerstenhaber cup product
on the Hochschild cohomology $HH^*(C^*(M)\,;C^*(M))$ for simply connected $M$.
However, some parts of their proof are technically difficult to justify. The
main aim of the present paper is to give detailed modification to a geometric
part of their proof. To do so, we set up an "up to higher homotopy" version of
McClure-Smith's cosimplicial product. We prove a structured version of
Cohen-Jones isomorphism in the category of symmetric spectra.
