Biequivalences in tricategories

TL;DR

This paper proves that internal biequivalences in tricategories can be extended to biadjoint biequivalences and explores applications in transporting monoidal structures and coherently choosing inverses in monoidal bicategories.

Contribution

It establishes that every internal biequivalence in a tricategory is part of a biadjoint biequivalence, providing new tools for structure transport and coherence in higher categories.

Findings

Internal biequivalences are part of biadjoint biequivalences in tricategories.

Applications include transporting monoidal structures.

Coherent choices of inverses in monoidal bicategories are achieved.

Abstract

We show that every internal biequivalence in a tricategory T is part of a biadjoint biequivalence. We give two applications of this result, one for transporting monoidal structures and one for equipping a monoidal bicategory with invertible objects with a coherent choice of those inverses.