  It is shown that the cochain complex of relative Hochschild A-valued cochains
of a depth two extension A | B under cup product is isomorphic as a
differential graded algebra with the Amitsur complex of the coring S = End
{}_BA_B over the centralizer R = A^B with grouplike element 1_S, which itself
is isomorphic to the Cartier complex of S with coefficients in the
(S,S)-bicomodule R^e. This specializes to finite dimensional algebras,
H-separable extensions and Hopf-Galois extensions.
