$ω$-weak equivalences between weak $ω$-categories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911112636661760 |
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| author | Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki |
| author_facet | Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_13240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $ω$-weak equivalences between weak $ω$-categories Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki Category Theory 18N65, 18N40, 18N20 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. |
| title | $ω$-weak equivalences between weak $ω$-categories |
| topic | Category Theory 18N65, 18N40, 18N20 |
| url | https://arxiv.org/abs/2406.13240 |