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.
Read more about Quiver (mathematics): Definition, Category-theoretic Definition, Path Algebra, Representations of Quivers, Gabriel's Theorem
Famous quotes containing the word quiver:
“The bud of the apple is desire, the down-falling gold,
The catbird’s gobble in the morning half-awake
These are real only if I make them so. Whistle
For me, grow green for me and, as you whistle and grow green,
Intangible arrows quiver and stick in the skin
And I taste at the root of the tongue the unreal of what is real.”
—Wallace Stevens (1879–1955)