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

TL;DR

This paper demonstrates that a specific $ ext{ extomega}$-category serves as a comprehensive model for fully coherent walking $ ext{ extomega}$-equivalence, with truncated versions modeling finite cases.

Contribution

It establishes a new model for fully coherent walking $ ext{ extomega}$-equivalence and its finite truncations, advancing the understanding of higher category theory.

Findings

Proves the $ ext{ extomega}$-category models fully coherent walking $ ext{ extomega}$-equivalence.

Provides truncated models for finite $n$-equivalences.

Connects the constructed model to previous work by the third and fourth authors.

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 $n\geq1$.