Example 8.4.1.3. Let $\operatorname{Cat}$ denote the ordinary category whose objects are small categories and whose morphisms are functors, and let $\operatorname{{\bf \Delta }}\subset \operatorname{Cat}$ be the simplex category. Proposition 1.3.3.1 asserts that the restricted Yoneda embedding
\[ \operatorname{Cat}\rightarrow \operatorname{Fun}( \operatorname{{\bf \Delta }}^{\operatorname{op}}, \operatorname{Set}) = \operatorname{Set_{\Delta }}\quad \quad \operatorname{\mathcal{C}}\mapsto \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) \]
is fully faithful, so that $\operatorname{{\bf \Delta }}$ is a dense subcategory of $\operatorname{Cat}$.