Finite Example?

Graph

• \(\ob{G}\) are vertices
• \(\hom{G}\) each path
• ∘ is path concatenation

• \(\ob{G}=\{X,Y,Z\}\),
• \(\hom{G}=\{ε,α,β,γ,αβ,βγ,...\}\)
• \(αβ∘γ=αβγ\)