(\omega\)-weak equivalences between weak \(\omega\)-categories

• Published in: arXiv.org
• Main Authors: Fujii, Soichiro, Hoshino, Keisuke, Maehara, Yuki
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 24.08.2024
• Subjects: Categories; Equivalence
• ISSN: 2331-8422

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