Kerodon

Example 8.4.1.14. Let $\operatorname{Cat}$ denote the (ordinary) category of small categories. Then the simplex category $\operatorname{{\bf \Delta }}$ is a dense full subcategory of $\operatorname{Cat}$ (Example 8.4.1.3), and $\operatorname{{\bf \Delta }}_{\leq 1}$ is a dense full subcategory of $\operatorname{{\bf \Delta }}$ (Exercise 8.4.1.4). However, $\operatorname{{\bf \Delta }}_{\leq 1}$ is not a dense full subcategory of $\operatorname{Cat}$ (Exercise 8.4.1.12).