Weak vertical composition II: totalities

TL;DR

This paper advances the understanding of semi-strict tricategories with weak vertical composition by establishing a biadjoint biequivalence with braided monoidal categories, enriching the categorical framework.

Contribution

It constructs a 2-category of doubly-degenerate semi-strict tricategories and proves a biadjoint biequivalence with the 2-category of braided monoidal categories.

Findings

Established a 2-category of doubly-degenerate semi-strict tricategories.

Proved a biadjoint biequivalence with braided monoidal categories.

Enhanced the categorical understanding of weak vertical composition.

Abstract

We continue our study of semi-strict tricategories in which the only weakness is in vertical composition. We assemble the doubly-degenerate such tricategories into a 2-category, defining weak functors and transformations. We exhibit a biadjoint biequivalence between this 2-category and the 2-category of braided (weakly) monoidal categories, braided (weakly) monoidal functors, and monoidal transformations.