Linear quiver

A $𝕂$ -linear quiver $Γ$ is a quiver whose vertices $Γ 𝑉$ are $𝕂$ -vector spaces and whose edges $Γ 𝐸$ are $𝕂$ -linear maps such that source and target are the domain and codomain respectively. cat It follows a linear quiver is a Subquiver of some small subcategory of Category of vector spaces.