Remark 8.6.0.3. The commutativity of the diagram (8.74) is not immediately obvious: the notions of cartesian conjugacy and cocartesian duality have separate definitions that are a priori unrelated to one another. We will maintain this separation in our exposition: the portions of this section which discuss conjugate fibrations (§8.6.1, §8.6.2, and §8.6.3) can be read independently of those which discuss dual fibrations (§8.6.4, §8.6.5, and §8.6.7). Only in §8.6.6 will we consider both notions simultaneously.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$