Nerves and cones of free loop-free ω-categories

Published 1 Mar 2021 in math.AT and math.CT | (2103.01066v2)

Abstract: We show that the complicial nerve construction is homotopically compatible with two flavors of cone constructions when starting with an $\omega$-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.

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