Nerves and cones of free loop-free ω-categories

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.

v2: restructured the paper improving exposition, included details on the second type of cone

References in corpus (3)

• A homotopy coherent cellular nerve for bicategories
• An $(\infty ,2)$-categorical pasting theorem
• Orientals as free weak $\omega$-categories