Category theory MOC

Underlying quiver

Let 𝖢 be a small category. The underlying quiver 𝑈(𝖢) is the quiver whose vertices are Ob⁡(𝖢) and whose edges are the morphisms of 𝖢, #m/def/cat such that if 𝑓 ∈𝖢(𝑋,𝑌) ⟺ 𝑓 ∈𝑈(𝖢)(𝑋,𝑌). Its left-adjoint is the Free category.

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