Coherence for adjunctions in a $3$-category via string diagrams

TL;DR

This paper introduces a method to extend any adjunction in a strict 3-category to a coherent form using string diagrams, ensuring a unique extension.

Contribution

It provides a formal definition of coherent adjunctions in strict 3-categories and demonstrates their construction via string diagrams, establishing essential uniqueness.

Findings

Any adjunction can be extended to a coherent adjunction.

The extension to a coherent adjunction is essentially unique.

String diagrams effectively illustrate the coherence process.

Abstract

We define a coherent adjunction in a strict $3$-category and we use string diagrams to show that any adjunction can be extended to a coherent adjunction in an essentially unique way.