Remark 7.7.2.2. In the situation of Notation 7.7.2.1, there is a canonical isomorphism $\operatorname{Fun}_{ / \operatorname{\mathcal{C}}}( K, \operatorname{\mathcal{E}}) \xleftarrow {\sim } \operatorname{Fun}_{ / K }( K, K \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}})$ of simplicial sets, which restricts to an isomorphism of $\operatorname{Fun}^{\operatorname{ACart}}_{/\operatorname{\mathcal{C}}}(K, \operatorname{\mathcal{E}})$ with the full subcategory
\[ \operatorname{Fun}^{\operatorname{Cart}}_{ / K}(K, K \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}) \subseteq \operatorname{Fun}_{ / K }( K, K \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}) \]
of Variant 5.3.1.11.