John wrote:
>These days we use 'categorification' to mean the process of taking math done with equations and boosting it up to math done with isomorphisms, equivalences, or other such things

It is interesting to learn more about the process of 'decategorification', when you lifted to some higher abstraction level, found structures which suit your purposes, and then need to find come concrete "implementations" and "substrates" which have this structure. Maybe there is some nice (introductory) read with examples?