Freely adding adjoints to (∞,n)-categories and the walking adjunction

The goal of this talk is to give a gentle introduction to adjunctions in the higher-categorical setting. After reviewing the main definitions, we will explain how to freely adjoin adjoints to an (∞,n)-category.
Time permitting, we will show how this construction can be used to recover a result of Riehl and Verity with a model-independent proof.