Directed graphs | Category theory | Representation theory

Quiver (mathematics)

In graph theory, 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 the underlying structure of a category, but without composition or a designation of identity morphisms. That is, there is a forgetful functor from Cat to Quiv. Its left adjoint is a free functor which, from a quiver, makes the corresponding free category. (Wikipedia).

Quiver (mathematics)
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Related pages

Category of sets | Dynkin diagram | Set theory | ADE classification | Vector space | Associative algebra | Derived noncommutative algebraic geometry | Forgetful functor | Free functor | Root system | Quiver diagram | Natural transformation | Representation theory | Projective module | Group ring | Linear map | Graph algebra | Mathematics | Vertex (graph theory) | Field (mathematics) | Incidence algebra | Category theory | Category (mathematics) | Morita equivalence | Morphism | Functor | Functor category | Approximate identity | Free category | Semi-invariant of a quiver | Directed graph | Adhesive category | Opposite category | Toric variety | Module (mathematics)