Quiver

Summary

A quiver is a directed graph in which several arrows between the same two vertices and loops at a vertex are allowed. Quivers are the combinatorial input of the representation theory of algebras. A representation of a quiver places a vector space at each vertex and a linear map along each arrow. Every quiver gives a path algebra, and many finite-dimensional algebras are quotients of path algebras. In category theory, a quiver is the underlying data of a category without composition.