Kerodon

Example 4.3.2.12. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{E}}$ be categories and let $S$ be an object of $\operatorname{\mathcal{E}}$. Applying Proposition 4.3.2.10 in the case $\operatorname{\mathcal{D}}= [0]$, we see that functors from $\operatorname{\mathcal{C}}$ to the slice category $\operatorname{\mathcal{E}}_{/S}$ can be identified with functors $U: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow \operatorname{\mathcal{E}}$ which carry the cone point of $\operatorname{\mathcal{C}}^{\triangleright }$ to the object $S$.