Let be a (commutative) field and a -algebra.
An -coring is semi-transitive if the category of -comodules which are finitely generated as modules over
It appears that semi-transitive corings are those corings which can be reconstructed from fiber functors on categories which are artinian, noetherian and with finite dimensional hom-spaces.
A. Bruguières, Théorie tannakienne non commutative, Comm. Algebra 22, 5817–5860, 1994
K. Szlachanyi, Fiber functors, monoidal sites and Tannaka duality for bialgebroids, arxiv/0907.1578