Curved differential graded algebras and corings

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.