Quiver subrepresentation

A quiver representation $𝐺 : Γ ―― \to 𝖵 𝖾 𝖼 𝗍 𝕂$ is called a subrepresentation of $𝐹 : Γ ―― \to 𝖵 𝖾 𝖼 𝗍 𝕂$ iff for all $𝑥 \in Γ 𝑉$ , $𝐺 (𝑥) \leq 𝕂 𝐹 (𝑥)$ is a $𝕂$ -vector subspace and $𝐹 (𝛼) : 𝐹 (𝑠 𝑎) \to 𝐺 (𝑡 𝑎)$ restricts to $𝐺 (𝛼) : 𝐺 (𝑠 𝑎) \to 𝐺 (𝑡 𝑎)$ . quiv Thus as $𝐺$ corresponds to a $𝕂 [Γ ――]$ -submodule.