  We study serial coalgebras by means of their valued Gabriel quivers. In
particular, Hom-computable and representation-directed coalgebras are
characterized. The Auslander-Reiten quiver of a serial coalgebra is described.
Finally, a version of Eisenbud-Griffith theorem is proved, namely, every
subcoalgebra of a prime, hereditary and strictly quasi-finite coalgebra is
serial.
