What are some illustrating examples of functors $\mathcal{E} \to \mathcal{B}$ which are neither a fibration nor an opfibration?
I've found many positive examples but I'm blanking out on negative ones, and they usually help to build a better intuition.
By fibration here I mean Grothendieck fibration, to be clear.
How about the functor $1 \to 2$ (numbers $n$ being seen as final ordinals, say, $\{0 <\ldots < n-1\}$, themselves seen as categories) picking $1$?