Example 10.3.0.8. Let $\operatorname{\mathcal{C}}$ be the category of partially ordered sets (with morphisms given by nondecreasing functions). Then $\operatorname{\mathcal{C}}$ is not regular: it satisfies conditions $(1)$ and $(2)$ of Definition 10.3.0.6, but does not satisfy condition $(3)$ (see Exercise 10.3.2.16).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$