  Let $(Q,\mathfrak n,k)$ be a commutative local Noetherian ring, $f_1,\dots,
f_c$ a $Q$-regular sequence in $\mathfrak n$, and $R=Q/(f_1,\dots,f_c)$. Given
a complex of finitely generated free $R$-modules, we give a construction of a
complex of finitely generated free $Q$-modules having the same homology. A key
application is when the original complex is an $R$-free resolution of a
finitely generated $R$-module. In this case our construction is a sort of
converse to a construction of Eisenbud-Shamash yielding a free resolution of an
$R$-module $M$ over $R$ given one over $Q$.
