Example 4.2.7. A set $C$ gives rise to a groupoid $\mathcal{C}$ defined as follows: As objects we take $\mathop{\mathrm{Ob}}\nolimits (\mathcal{C}) := C$ and for morphisms we take $\mathop{\mathrm{Mor}}\nolimits (x, y)$ empty if $x\neq y$ and equal to $\{ \text{id}_ x\} $ if $x = y$.

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