Weakly invertible cells in a weak $ω$-category
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917842655379456 |
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| author | Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki |
| author_facet | Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki |
| contents | We study weakly invertible cells in weak $ω$-categories in the sense of Batanin-Leinster, adopting the coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $ω$-category are closed under globular pasting. Using this, we generalise elementary properties of weakly invertible cells known to hold in strict $ω$-categories to weak $ω$-categories, and show that every weak $ω$-category has a largest weak $ω$-subgroupoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14907 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weakly invertible cells in a weak $ω$-category Fujii, Soichiro Hoshino, Keisuke Maehara, Yuki Category Theory 18N65, 18N20 We study weakly invertible cells in weak $ω$-categories in the sense of Batanin-Leinster, adopting the coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $ω$-category are closed under globular pasting. Using this, we generalise elementary properties of weakly invertible cells known to hold in strict $ω$-categories to weak $ω$-categories, and show that every weak $ω$-category has a largest weak $ω$-subgroupoid. |
| title | Weakly invertible cells in a weak $ω$-category |
| topic | Category Theory 18N65, 18N20 |
| url | https://arxiv.org/abs/2303.14907 |