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Nerves and cones of
free loop-free $\omega$-categories
Andrea Gagna, Viktoriya Ozornova and Martina Rovelli |
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Vol. 5 (2023), No. 2, 273–326
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Abstract |
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We show that the complicial nerve construction is homotopically compatible with two flavors of cone constructions when starting with an -category that is suitably free and loop-free. An instance of the result recovers the fact that the standard -simplex is equivalent to the complicial nerve of the -oriental. |
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Keywords
$\omega$-categories, $(\infty,\infty)$-categories, cone,
nerve, complicial set, augmented directed chain complexes
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Mathematical Subject Classification
Primary: 18N30
Secondary: 18N65, 55U10, 55U15
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Milestones
Received: 11 January 2022
Revised: 30 September 2022
Accepted: 17 October 2022
Published: 4 June 2023
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Authors |
| Andrea Gagna | |
| Institute of Mathematics Czech Academy of Sciences Prague Czech Republic |
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| Viktoriya Ozornova | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| Martina Rovelli | |
| Department of Mathematics and
Statistics University of Massachusetts Amherst MA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
