# Kerodon

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Example 9.10.1.6. Let $S = \Delta ^0$. Then the simplicial category $\operatorname{Cart}(S) = \operatorname{CCart}(S)$ can be described as follows:

• An objects of $\operatorname{Cart}(S)$ is a small $\infty$-category $\operatorname{\mathcal{C}}$.

• If $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ are small $\infty$-categories, then $\operatorname{Hom}_{\operatorname{Cart}(S)}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})_{\bullet } = \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})^{\simeq }$ is the core of the functor $\infty$-category $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$.

In other words, $\operatorname{Cart}(S)$ can be identified with the simplicial category $\operatorname{QCat}$ of Construction 5.6.4.1.