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arXiv · 2608.28355

About the contractibility of the walking coinductive equivalence

Viktoriya Ozornova·Martina Rovelli·Tashi Walde
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Abstract

We study the marked simplicial set obtained as the Roberts-Street nerve of the walking coinductive equivalence. We show that it is a non-contractible saturated complicial set for which all of its finite truncations are contractible. When regarding saturated complicial sets as a model for right $(\infty,\infty)$-categories, it represents a concrete and explicit example of a right $(\infty,\infty)$-category that is itself non-contractible, but whose reflection to a left $(\infty,\infty)$-category is contractible.

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Viktoriya Ozornova, Martina Rovelli, Tashi Walde. 2026-08-28. About the contractibility of the walking coinductive equivalence. https://arxiv.org/abs/2608.28355

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