ω-weak equivalences between weak ω-categories

We study ω -weak equivalences between weak ω -categories in the sense of Batanin–Leinster. Our ω -weak equivalences are strict ω -functors satisfying essential surjectivity in every dimension, and when restricted to those between strict ω -categories, they coincide with the weak equivalences in the model category of strict ω -categories defined by Lafont, Métayer, and Worytkiewicz. We show that the class of ω -weak equivalences has the 2-out-of-3 property. We also consider a generalisation of ω -weak equivalences, defined as weak ω -functors (in the sense of Garner) satisfying essential surjectivity, and show that this class also has the 2-out-of-3 property.