Kerodon

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

Remark 5.1.1.9. In the situation of Definition 5.1.1.8, the morphism $g$ is given by contravariant transport along $e$ if and only if the opposite map $g^{\operatorname{op}}: X_{s'}^{\operatorname{op}} \rightarrow X_{s}^{\operatorname{op}}$ is given by covariant transport along $e$ with respect to the left fibration $q^{\operatorname{op}}: X^{\operatorname{op}} \rightarrow S^{\operatorname{op}}$.