Example 10.3.1.28. Let $\operatorname{\mathcal{C}}$ be the $1$-dimensional simplicial set associated to the directed graph depicted in the diagram
\[ \xymatrix@R =50pt@C=50pt{ A \ar [r] \ar [d] & X \\ Y & B, \ar [l] \ar [u] } \]
and let $\operatorname{\mathcal{C}}^{0}_{/X} \subseteq \operatorname{\mathcal{C}}_{/X}$ be the sieve spanned by the objects $A$ and $B$. Then $\operatorname{\mathcal{C}}^{0}_{/X}$ is dense when regarded as a full category of $\operatorname{\mathcal{C}}_{/X}$ (in the sense of Definition 8.4.1.5), but not when regarded as a sieve on $X$ (in the sense of Definition 10.3.1.26).