A Quillen adjunction between globular and complicial approaches to (∞,n)-categories

We prove the compatibility between the suspension construction and the complicial nerve of ω-categories. As a motivating application, we produce a Quillen pair between the models of (∞,n)-categories given by Rezk's complete Segal Θn-spaces and Verity's n-complicial sets.

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Bibliographische Detailangaben
Veröffentlicht in:	Advances in mathematics (New York. 1965) 2023-05, Vol.421, p.108980, Article 108980
Hauptverfasser:	Ozornova, Viktoriya, Rovelli, Martina
Format:	Artikel
Sprache:	eng
Schlagworte:	[formula omitted]-categories Complete Segal [formula omitted]-spaces Complicial nerve Complicial sets n-categories Suspension of n-categories
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Beschreibung
Zusammenfassung:	We prove the compatibility between the suspension construction and the complicial nerve of ω-categories. As a motivating application, we produce a Quillen pair between the models of (∞,n)-categories given by Rezk's complete Segal Θn-spaces and Verity's n-complicial sets.
ISSN:	0001-8708 1090-2082
DOI:	10.1016/j.aim.2023.108980