Example 5.6.1.10. Let $\operatorname{\mathcal{C}}$ be a category and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \mathbf{Cat}$ denote the (strict) functor given on objects by the formula $\mathscr {F}(C) = \operatorname{\mathcal{C}}_{/C}$. Then the category of elements $\int _{\operatorname{\mathcal{C}}} \mathscr {F}$ can be identified with the arrow category $\operatorname{Fun}( [1], \operatorname{\mathcal{C}})$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$