Editing Quiver (mathematics) (section)

==Definition==

A quiver {{math|Γ}} consists of:
* The set {{mvar|V}} of vertices of {{math|Γ}}
* The set {{mvar|E}} of edges of {{math|Γ}}
* Two functions: {{tmath|s:E \to V}} giving the ''start'' or ''source'' of the edge, and another function, {{tmath|t:E \to V}} giving the ''target'' of the edge.

This definition is identical to that of a [[multidigraph]].

A [[morphism]] of quivers is a mapping from vertices to vertices which takes directed edges to directed edges. Formally, if <math>\Gamma=(V,E,s,t)</math> and <math>\Gamma'=(V',E',s',t')</math> are two quivers, then a morphism <math>m=(m_v, m_e)</math> of quivers consists of two functions <math>m_v: V\to V'</math> and <math>m_e: E\to E'</math> such that the following [[commuting diagram|diagrams commute]]:  

[[File:Quiver Morphism Start Diagram.svg|frameless|]]
[[File:Quiver Morphism Target Diagram.svg|frameless|]]

That is,
:<math>m_v \circ s = s' \circ m_e</math>
and
:<math>m_v \circ t = t' \circ m_e</math>