Corollary 1.1.5.8. Let $\operatorname{\mathcal{C}}$ be a category. Then the evaluation functor
\[ \operatorname{ev}_{0}: \operatorname{Fun}( \operatorname{{\bf \Delta }}^{\operatorname{op}}, \operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}\quad \quad X_{\bullet } \mapsto X_0 \]
admits a left adjoint, given on objects by the formation of constant simplicial objects $C \mapsto \underline{C}_{}$ described in Construction 1.1.5.2.