Serial coalgebras and their valued Gabriel quivers

We study serial coalgebras by means of their valued Gabriel quivers. In particular, Hom-computable and representation-directed serial 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.