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Nerves and cones of free loop-free $\omega$-categories

Andrea Gagna, Viktoriya Ozornova and Martina Rovelli

Vol. 5 (2023), No. 2, 273–326

We show that the complicial nerve construction is homotopically compatible with two flavors of cone constructions when starting with an ω-category that is suitably free and loop-free. An instance of the result recovers the fact that the standard m-simplex is equivalent to the complicial nerve of the m-oriental.

$\omega$-categories, $(\infty,\infty)$-categories, cone, nerve, complicial set, augmented directed chain complexes
Mathematical Subject Classification
Primary: 18N30
Secondary: 18N65, 55U10, 55U15
Received: 11 January 2022
Revised: 30 September 2022
Accepted: 17 October 2022
Published: 4 June 2023
Andrea Gagna
Institute of Mathematics
Czech Academy of Sciences
Czech Republic
Viktoriya Ozornova
Max Planck Institute for Mathematics
Martina Rovelli
Department of Mathematics and Statistics
University of Massachusetts Amherst
United States