تقرير
$\omega$-weak equivalences between weak $\omega$-categories
| العنوان: | $\omega$-weak equivalences between weak $\omega$-categories |
|---|---|
| المؤلفون: | Fujii, Soichiro, Hoshino, Keisuke, Maehara, Yuki |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Category Theory, 18N65, 18N40, 18N20 |
| الوصف: | 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, M\'etayer, 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. Comment: 25 pages. Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.13240 |
| رقم الأكسشن: | edsarx.2406.13240 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |