Quiv

**$Quiv$** or **$DiGraph$** is the category of quivers or (as category theorists often call them) directed graph.

We can define a quiver to be a functor $G\colon X^{op} \to Set$, where $X^{op}$ is the category with an object $0$, an object $1$ and two morphisms $s, t\colon 1 \to 0$, along with identity morphisms. This lets us efficiently define $Quiv$ as the category of presheaves on $X$, where:

- objects are functors $G\colon X^{op} \to C$,
- morphisms are natural transformations between such functors.

In other words, $Quiv$ is the functor category from this $X^{op}$ to Set.

category: category

Revised on February 13, 2011 19:42:53
by Toby Bartels
(75.88.68.70)