Quiver representation theory MOC

Quiver

A quiver is, loosely speaking, a category minus the algebra #m/def/quiv — the oidification of a set.

Category theoretic definition

The walking quiver to is the category consisting of objects of edges and nodes and non-identity morphism of source and target. A quiver is then a functor .

Notation

We use the notation

to denote the set of edges between vertices and . As an abuse, we often identify with its underlying general graph. See Equivalence of quivers and general graphs.

• A morphism of the free category is called a path.

See also

• Quiver representation theory MOC
• Adjacency matrix

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