PreprintarXiv licencearXiv
About the contractibility of the walking coinductive equivalence
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 (∞,∞)-categories, it represents a concrete and explicit example of a right (∞,∞)-category that is itself non-contractible, but whose reflection to a left (∞,∞)-category is contractible.
Related
- On an open question about the equivalence of monotone maximality and surjectivity condition in CAT(0) spaces: Negative and partially positive answers
- Coinductive reasoning for parametrized functors and monads
- Homological obstructions to local contractibility in noncollapsed Ricci limits
- Exchange complexes and contractibility of the complex of incompressible Seifert surfaces
- Free bifibrations of (∞,2)-categories, 2-simplicial objects and the walking adjunction
BibTeX
@misc{ozornova2026about,
title = {{About the contractibility of the walking coinductive equivalence}},
author = {Viktoriya Ozornova and Martina Rovelli and Tashi Walde},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28355},
eprint = {2608.28355},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28355},
}
RIS
TY - UNPB
TI - About the contractibility of the walking coinductive equivalence
AU - Viktoriya Ozornova
AU - Martina Rovelli
AU - Tashi Walde
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28355
UR - https://arxiv.org/abs/2608.28355
AB - 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 (∞,∞)-categories, it represents a concrete and explicit example of a right (∞,∞)-category that is itself non-contractible, but whose reflection to a left (∞,∞)-category is contractible.
ER -