International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 13, Article ID 47146, 16 pages
doi:10.1155/IJMMS/2006/47146

Irreducible morphisms, the Gabriel-valued quiver and colocalizations for coalgebras.

Abstract

Given a basic K-coalgebra C, we study the left Gabriel-valued quiver (QC,dC) of C by means of irreducible morphisms between indecomposable injective left C-comodules and by means of the powers radm of the radical rad of the category C-inj of the socle-finite injective left C-comodules. Connections between the valued quiver (QC,dC) of C and the valued quiver (QC¯,dC¯) of a colocalization coalgebra quotient fE:C→C¯ of C are established.