Gray-categories model algebraic tricategories

TL;DR

This paper demonstrates that localizing the category of Gray-categories at weak 3-equivalences yields a category equivalent to algebraic tricategories with pseudo-natural equivalences, advancing the understanding of higher categorical structures.

Contribution

It adapts existing techniques to establish an equivalence between localized Gray-categories and algebraic tricategories, clarifying their relationship.

Findings

Localization of GrayCat at weak 3-equivalences is equivalent to algebraic tricategories.

Provides a new perspective on the structure of higher categories.

Extends the understanding of Quillen model structures in higher category theory.

Abstract

Lack described a Quillen model structure on the category GrayCat of Gray-categories and Gray-functors, for which the weak equivalences are the weak 3-equivalences. In this note, we adapt the technique of Gurski, Johnson, and Osorno to show the localization of GrayCat at the weak equivalences is equivalent to the category of algebraic tricategories and pseudo-natural equivalence classes of weak 3-functors.