[[Quiver representation]]
# Path algebra

Given a [[quiver]] $\Gamma$ and [[commutative ring]] $R$, the **path algebra** $R \underline{\Gamma}$ is the [[Category ring]] of the [[free category]] $\underline \Gamma$. #m/def/quiv
If $\Gamma$ is finite, then $R\underline{\Gamma}$ is a finitely generated [[R-monoid]],

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