quiver

In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows between two vertices are allowed. Quivers are commonly used in representation theory: a representation  of a quiver assigns a vector space  to each vertex  of the quiver and a linear map  to each arrow . In category theory, a quiver can be understood to be the underlying structure of a category, but without composition or a designation of identity morphisms. That is, there is a forgetful functor from (the category of categories) to (the category of multidigraphs). Its left adjoint is a free functor which, from a quiver, makes the corresponding free category. Definition A quiver consists of: The set of vertices of The set of edges of Two functions: giving the start or source of the edge, and another function, giving the target of the edge.