$ω$-equifibrations between strict and weak $ω$-categories
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| Format: | Preprint |
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2025
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| author | Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki |
| author_facet | Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki |
| contents | We study $ω$-equifibrations between weak $ω$-categories in the sense of Batanin--Leinster. We define $ω$-equifibrations as a natural weak $ω$-categorical analogue of isofibrations between categories, and show that they can be characterised via the right lifting property with respect to a suitable set $J$ of strict $ω$-functors. The definition of $J$ involves the construction of a certain weak $ω$-category $\mathcal{E}^1$ which, roughly speaking, is freely generated by an equivalence 1-cell in a ``coherent'' manner. We show that the strict version of $\mathcal{E}^1$ coincides with Ozornova and Rovelli's coherent walking $ω$-equivalence $\widehat{ω\mathcal{E}}$. The $ω$-equifibrations between strict $ω$-categories coincide with the fibrations in the folk model structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_09849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $ω$-equifibrations between strict and weak $ω$-categories Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki Category Theory 18N65, 18N30, 18N40, 18N20 We study $ω$-equifibrations between weak $ω$-categories in the sense of Batanin--Leinster. We define $ω$-equifibrations as a natural weak $ω$-categorical analogue of isofibrations between categories, and show that they can be characterised via the right lifting property with respect to a suitable set $J$ of strict $ω$-functors. The definition of $J$ involves the construction of a certain weak $ω$-category $\mathcal{E}^1$ which, roughly speaking, is freely generated by an equivalence 1-cell in a ``coherent'' manner. We show that the strict version of $\mathcal{E}^1$ coincides with Ozornova and Rovelli's coherent walking $ω$-equivalence $\widehat{ω\mathcal{E}}$. The $ω$-equifibrations between strict $ω$-categories coincide with the fibrations in the folk model structure. |
| title | $ω$-equifibrations between strict and weak $ω$-categories |
| topic | Category Theory 18N65, 18N30, 18N40, 18N20 |
| url | https://arxiv.org/abs/2511.09849 |