Quiver (mathematics)

Quiver (mathematics)

In mathematics, a quiver is a directed graph where loops and multiple arrows between two vertices are allowed, i.e. a multidigraph. They are commonly used in representation theory: a representation, V, of a quiver assigns a vector space V(x) to each vertex x of the quiver and a linear map V(a) to each arrow a.

In category theory, a quiver can be understood to be a category without identity morphisms and composition. That is, there is a forgetful functor from Cat to Quiv. Its left adjoint is a functor that sends quivers to the free category.