Cores and localizations of $(\infty,\infty)$-categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918383508783104 |
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| author | Ozornova, Viktoriya Rovelli, Martina Walde, Tashi |
| author_facet | Ozornova, Viktoriya Rovelli, Martina Walde, Tashi |
| contents | We consider $(\infty,d)$-categories in the limit $d\to \infty$ via the core or localization functors that forget or invert higher non-invertible arrows, respectively. We compare the two resulting $(\infty,1)$-categories of $(\infty,\infty)$-categories and exhibit the localization-limit as a reflective localization of the core-limit.
On the side, we study intermediate localizations that arise from notions of invertibility that only emerge at $d=\infty$ such as the one defined by coinduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11005 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cores and localizations of $(\infty,\infty)$-categories Ozornova, Viktoriya Rovelli, Martina Walde, Tashi Algebraic Topology Category Theory 18N65, 18N55, 55U35 We consider $(\infty,d)$-categories in the limit $d\to \infty$ via the core or localization functors that forget or invert higher non-invertible arrows, respectively. We compare the two resulting $(\infty,1)$-categories of $(\infty,\infty)$-categories and exhibit the localization-limit as a reflective localization of the core-limit. On the side, we study intermediate localizations that arise from notions of invertibility that only emerge at $d=\infty$ such as the one defined by coinduction. |
| title | Cores and localizations of $(\infty,\infty)$-categories |
| topic | Algebraic Topology Category Theory 18N65, 18N55, 55U35 |
| url | https://arxiv.org/abs/2603.11005 |