Remark 5.6.1.2. The category of elements $\int _{\operatorname{\mathcal{C}}} \mathscr {F}$ was originally introduced by Grothendieck in [MR0217088]. For this reason, many authors refer to the category $\int _{\operatorname{\mathcal{C}}} \mathscr {F}$ as the *Grothendieck construction* on the functor $\mathscr {F}$.

$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$