Quiver bialgebras and monoidal categories

Hua-Lin Huang¹ ; Blas Torrecillas²

¹ School of Mathematics Shandong University Jinan 250100, China
² Department of Algebra and Analysis Universidad de Almería 04071 Almería, Spain

Colloquium Mathematicum, Tome 131 (2013) no. 2, pp. 287-300

Résumé

We study bialgebra structures on quiver coalgebras and monoidal structures on the categories of locally nilpotent and locally finite quiver representations. It is shown that the path coalgebra of an arbitrary quiver admits natural bialgebra structures. This endows the category of locally nilpotent and locally finite representations of an arbitrary quiver with natural monoidal structures from bialgebras. We also obtain theorems of Gabriel type for pointed bialgebras and hereditary finite pointed monoidal categories.

Détail

DOI : 10.4064/cm131-2-10

Mots-clés : study bialgebra structures quiver coalgebras monoidal structures categories locally nilpotent locally finite quiver representations shown path coalgebra arbitrary quiver admits natural bialgebra structures endows category locally nilpotent locally finite representations arbitrary quiver natural monoidal structures bialgebras obtain theorems gabriel type pointed bialgebras hereditary finite pointed monoidal categories