[001I] Construction 6.1.1·a.

Let $E$ be displayed over $B$; we define its total opposite $\TotOpCat{E}$ displayed over $\OpCat{B}$ as follows:

  1. An object of $\TotOpCat{E}\Sub{x}$ is given by an object of $E\Sub{x}$.

  2. Given $f : x \to y\in \OpCat{B}$, a displayed morphism $\bar{x}\to\Sub{f} \bar{y}$ in $\TotOpCat{E}$ is given by a displayed morphism $\bar{y}\to\Sub{f} \bar{x}$ in $E$.