[[Quiver representation theory MOC]]
# Quiver subrepresentation

A [[quiver representation]] $G : \underline{\Gamma} \to \Vect_{\mathbb{K}}$
is called a **subrepresentation** of $F : \underline \Gamma \to \Vect_{\mathbb{K}}$ iff for all $x \in \Gamma V$,
$G(x) \leq_{\mathbb{K}} F(x)$ is a $\mathbb{K}$-[[vector subspace]]
and $F(\alpha) : F(sa) \to G(ta)$ restricts to $G(\alpha) : G(sa) \to G(ta)$. #m/def/quiv 
Thus as $G$ corresponds to a $\mathbb{K}[\underline \Gamma]$-[[submodule]].


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#state/tidy | #lang/en | #SemBr