# Kerodon

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Remark 5.2.6.3. 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 5.2.6.1 and $\int ^{\operatorname{\mathcal{C}}^{\operatorname{op}}} \mathscr {F}$ is the category of elements introduced in Variant 5.2.6.2.