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

It has been conjectured since the 1980s that Verity’s $n$-complicial sets were a model for $(\mathrm{\infty },n)$-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.