International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 47146, 16 pages
Irreducible morphisms, the Gabriel-valued quiver and
colocalizations for coalgebras
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, Toruń 87-100, Poland
Received 22 December 2005; Revised 7 May 2006; Accepted 9 May 2006
Copyright © 2006 Daniel Simson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Given a basic -coalgebra , we study the left Gabriel-valued quiver of by means of irreducible morphisms between indecomposable injective left -comodules and by means of the powers of the radical of the category
- of the socle-finite injective left -comodules.
Connections between the valued quiver of and the valued quiver of a colocalization coalgebra quotient of are established.