# Kerodon

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

Remark 4.3.1.5. Variant 4.3.1.4 is formally dual to Construction 4.3.1.1. More precisely, if $S$ is an object of a category $\operatorname{\mathcal{C}}$, then we have a canonical isomorphism of categories

$(\operatorname{\mathcal{C}}_{/S})^{\operatorname{op}} \simeq (\operatorname{\mathcal{C}}^{\operatorname{op}})_{S/},$

where we view $S$ also as an object of the opposite category $\operatorname{\mathcal{C}}^{\operatorname{op}}$.