Equivalence of quivers and general graphs

The notions of general graph and quiver are similar, the only difference being that quivers have separate “identities” for each of their arcs, whereas general graphs keep track only of the number of arcs between given vertices. One can naturally construct a “forgetful functor” from $𝖰 𝗎 𝗂 𝗏$ to $𝖦 𝗋 𝗉 𝗁$ , which is made into a full Equivalence of categories. An elementary consequence of this is that isomorphism classes of quivers and graphs are essentially the same.

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