Let $k$ be a (commutative) field and $R$ a $k$-algebra.
An $R$-coring $C$ is semi-transitive if the category $M^C_f$ of $C$-comodules which are finitely generated as modules over $R$
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