Work

About the contractibility of the walking coinductive equivalence

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.28355

Authors: Ozornova, Viktoriya, Rovelli, Martina, Walde, Tashi

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Natural Sciences and Engineering Research Council of Canada

Awards: G1861350003, Model Comparisons and Foundational Developments in Higher Category Theory

OpenAlex ID: W7204850311

Cites: 3

Cited by: 1

Related to: 10