  A relationship between curved differential algebras and corings is
established and explored. In particular it is shown that the category of
semi-free curved differential graded algebras is equivalent to the category of
corings with surjective counits. Under this equivalence, comodules over a
coring correspond to integrable connections or quasi-cohesive curved modules,
while contramodules over a coring correspond to a specific class of curved
modules introduced and termed Z-divergences in here.
