The complicial model of $(\infty,\omega)$-categories

TL;DR

This paper proves that Verity's $n$-complicial sets serve as a valid model for $( abla, ext{infinity})$-categories, confirming a long-standing conjecture through detailed analysis of Gray operations across various categorical frameworks.

Contribution

It provides a rigorous proof confirming Verity's $n$-complicial sets as a model for $( abla, ext{infinity})$-categories, advancing the understanding of higher category theory.

Findings

Verity's $n$-complicial sets model $( abla, ext{infinity})$-categories

Analysis of Gray operations in strict $ ext{omega}$-categories

Connections established between complicial sets and enriched Segal precategories

Abstract

It has been conjectured since the 1980s that Verity's $n$-complicial sets were a model for $(\infty,n)$-categories. This text is dedicated to providing a positive answer to this conjecture. The proof of this result relies on a thorough study of Gray operations in (strict) $\omega$-categories, in complicial sets, and in enriched (stratified) Segal precategories.