A model for the coherent walking $\omega$-equivalence

Amar Hadzihasanovic; F\'elix Loubaton; Martina Rovelli; Viktoriya Ozornova

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A model for the coherent walking $\omega$-equivalence

Amar Hadzihasanovic, Félix Loubaton, Viktoriya Ozornova, Martina Rovelli

Category Theory · Submitted 22 Apr 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that a certain $\omega$-category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking $\omega$-equivalence.

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arXiv ID2404.14509 (version 1)

Pith IDEXDMQWFV, Pith's permanent record of this paper and its review

CitationAmar Hadzihasanovic, F\'elix Loubaton, Martina Rovelli, Viktoriya Ozornova. "A model for the coherent walking $\omega$-equivalence." arXiv:2404.14509 (2024). https://pith.science/paper/EXDMQWFV

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We prove that a certain $\omega$-category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking $\omega$-equivalence. Further, appropriate truncations of it give models for the fully coherent walking $n$-equivalence for each $n\geq1$.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove that a certain $\omega$-category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking $\omega$-equivalence.	result 0.89	0.93	0.93	asserted 1.00
s1	Further, appropriate truncations of it give models for the fully coherent walking $n$-equivalence for each $n\geq1$.	result 0.93	0.81	0.12	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We prove that a certain $\omega$-category, which was constructed in previous work by the third and fourth author, is a model for the fully coherent walking $\omega$-equivalence. Further, appropriate truncations of it give models for the fully coherent walking $n$-equivalence for each $n\geq1$.

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2 arXiv papers cite this in 6 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Builds on it 1 paper

We note already that an analogue of the main theorem of [ref] holds in the $(∞, n)$model structure by purely formal reasons.

Model structures for diagrammatic $(\infty, n)$-categories · Unmarked model structures · 0.87

What it cites · 15 sentences without a confident label

Uses the method or tool of 1 paper

Using the theory of marked $ω$-categories from [ref] , we show in this paper as <ref> that $ω$ is a contractible $ω$-category.

An inductive model structure for strict $\infty$-categories · Introduction · 1.00

Cites as background 5 papers

We briefly recall some notions on marked $ω$-categories from [ref] that will be needed in this paper.

An inductive model structure for strict $\infty$-categories · Marked -categories · 1.00
Properties of such notion of sameness, which we refer to as $ω$-equivalence or $n$-equivalence, have been studied e.g. in [ref] .

Diagrammatic sets and rewriting in weak higher categories · Introduction · 0.96
Properties of such notion of sameness, which we refer to as $ω$-equivalence or $n$-equivalence, have been studied e.g. in [ref] .

Coinductive Invertibility in Higher Categories · Introduction · 0.96

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