Flagged higher categories

David Ayala; John Francis

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arXiv · 1801.08973

Flagged higher categories

David Ayala·John Francis

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Abstract

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 $i$.

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David Ayala, John Francis. 2018-01-26. Flagged higher categories. https://arxiv.org/abs/1801.08973

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