This master thesis extends change of enrichment from the ordinary setting of categories enriched over a monoidal category to that of a \(2\)-category enriched over a monoidal \(2\)-category.
After giving the construction, we show that it is functorial.
We then consider represented \(2\)-functors \(\ca(C,-) \colon \ca \to \Cat\) and demonstrate that the structure needed to change enrichment along these functors is equivalent to the structure of a comonoid on the representing object \(C\).
As a corollary, we see that there is a canonical natural transformation \((-)_0 \Rightarrow \operatorname{ChEn}(-,F)\) from the underlying bicategory functor \((-)_0\) to the functor that changes the enrichment along a fixed functor \(F\).
Finally, we describe how an extended version of the bicategory of spans can be formally constructed via change of enrichment.