Graph theory MOC

Category of quivers

The category of quivers 𝖰𝗎𝗂𝗏 is a category where an object is a quiver and a morphism is a quiver homomorphism. cat It is therefore identical to the Functor category {𝖰}, where 𝖰 is the walking quiver.

Important functors

• There is a natural way 𝖰𝗎𝗂𝗏 →𝖦𝗋𝖺𝗉𝗁 to associate every quiver to an “underlying” general graph, see Equivalence of quivers and general graphs.
• This factorizes the forgetful functor V into the underlying vertex set.
• See Underlying quiver and Free category

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