Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 5.5.1.3. Let $\operatorname{\mathcal{C}}$ be a category and let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set}$ be a functor. Then we have a canonical isomorphism of categories

\[ (\int _{\operatorname{\mathcal{C}}} \mathscr {F})^{\operatorname{op}} \simeq (\int ^{\operatorname{\mathcal{C}}^{\operatorname{op}}} \mathscr {F}), \]

where $\int _{\operatorname{\mathcal{C}}} \mathscr {F}$ is the category of elements introduced in Construction 5.5.1.1 and $\int ^{\operatorname{\mathcal{C}}^{\operatorname{op}}} \mathscr {F}$ is the category of elements introduced in Variant 5.5.1.2.