Quiver bialgebras and monoidal categories
Tom 131 / 2013
Colloquium Mathematicum 131 (2013), 287-300 MSC: Primary 16T10; Secondary 18D10, 16G20. DOI: 10.4064/cm131-2-10
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.