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arXiv · 2603.11005

Cores and localizations of $(\infty,\infty)$-categories

Viktoriya Ozornova·Martina Rovelli·Tashi Walde
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Abstract

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.

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Viktoriya Ozornova, Martina Rovelli, Tashi Walde. 2026-03-11. Cores and localizations of $(\infty,\infty)$-categories. https://arxiv.org/abs/2603.11005

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