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Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors ${\Omega }_{\lambda }\left(R\right)$ and ℓ(R) together with algebra homomorphisms $e:{\Omega }_{\lambda }\left(R\right)\to H*\left(\Lambda X\right)$ and $\psi :\ell \left(R\right)\to H*\left(E{S}^1{\times }_{S^1}\Lambda X\right)$. When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.