2.5. Fiber categories and vertical maps [0005]

Let $E$ be a category displayed over $B$. A vertical map in $E$ is defined to be one that lies over the identity map in $B$. For every $b\in B$, there the collection $E\Sub{b}$ of displayed objects has the structure of a category; in particular, we set $E\Sub{b}(u,v)$ to be the collection of vertical maps $u\to\Sub{\Idn{b}}v$.