[002Z] Construction 6.1.3·a.

Let $B$ be a category. Define the displayed category $\overline{B}$ over $B$ as follows:

  1. For $x\in B$, define $\overline{B}\Sub{x}$ as the collection of pairs $(\bar{x}\in B,p\Sub{x}:x\to\bar{x})$.
  2. For $f : x\to y\in B$, define $\overline{B}\Sub{f}$ to be the collection of commuting squares in the following configuration: