Abstract
We introduce flagged (∞, n)-categories and prove that they are equivalent to Segal sheaves on Joyal’s category Θ n. 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 as an instance of Koszul duality. 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.
| Original language | English (US) |
|---|---|
| Title of host publication | Contemporary Mathematics |
| Publisher | American Mathematical Society |
| Pages | 137-173 |
| Number of pages | 37 |
| DOIs | |
| State | Published - Jan 1 2018 |
Publication series
| Name | Contemporary Mathematics |
|---|---|
| Volume | 718 |
| ISSN (Print) | 0271-4132 |
| ISSN (Electronic) | 1098-3627 |
Keywords
- (∞, n)-categories
- Cech nerve
- Flagged higher categories
- Groupoid objects
- Higher categories
- Segal spaces
- Univalence
ASJC Scopus subject areas
- Mathematics(all)
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Cite this
Ayala, D., & Francis, J. (2018). Flagged higher categories. In Contemporary Mathematics (pp. 137-173). (Contemporary Mathematics; Vol. 718). American Mathematical Society. https://doi.org/10.1090/conm/718/14489