Example 10.3.4.11. Let $\operatorname{\mathcal{C}}$ be (the nerve of) the category of partially ordered sets. Then Exercise 10.3.2.16 supplies an example of a quotient morphism $f: Q \twoheadrightarrow [2]$ in $\operatorname{\mathcal{C}}$ which is not a universal quotient morphism.
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