Flagged higher categories

الأصل · EN

We introduce flagged (∞,n)-categories and prove that they are equivalent to Segal sheaves on Joyal's category Θₙ. As such, flagged (∞,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 (∞,n)-categories as stacks on (∞,n)-categories that satisfy descent with respect to colimit diagrams that do not generate invertible i-morphisms for any i.