  We introduce \emph{flagged $(\infty,n)$-categories} and prove that they are
equivalent to Segal sheaves on Joyal's category ${\mathbf\Theta}_n$. As such,
flagged $(\infty,n)$-categories provide a model-independent formulation of
Segal sheaves. This result generalizes the statement that $n$-groupoid objects
in spaces are effective, as we explain and contextualize. Along the way, we
establish a useful expression for the univalent-completion of such a Segal
sheaf. Finally, we conjecture a characterization of flagged
$(\infty,n)$-categories as stacks on $(\infty,n)$-categories that satisfy
descent with respect to colimit diagrams that do not generate invertible
$i$-morphisms for any $i$.
