  We present a criterion for $2$-final $(2,1)$-functors, analoguous to the
classical one for final $1$-functor: a $(2,1)$-functor $F \colon A \to B$ is
$2$-final if and only if, for any object $b$ of $B$, the slice $(2,1)$-category
$b / F$ is nonempty, connected and simply connected. We also give a
combinatorial presentation of paths and homotopies of paths in a
$(2,1)$-category.
