Michael - yes! That's one of the main lessons of category theory! These days we use ['categorification'](https://en.wikipedia.org/wiki/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.

A lot of old math, done with equations, really deserves to be improved in this way!

A lot of old math, done with equations, really deserves to be improved in this way!