Where do adjoint functors occur in CS? They occur in advanced algebra, and they occur in topology, but where else? And indeed, the fact that they preserve limits/colimits may help speed up communication and thinking. But I'm not seeing CS connections here.
>The first example is trivial, and serves as an illustrative but useless example (which I don't need).
Yep. Most of the example of adjoints trivial if you know the field of math where they are used. The interesting part is why it happens almost everywhere.
Another one is a free monoid. With pair of forgetful/free monoid functors. It sounds a bit mathematical but for type T free monoid is a List<T> in a programming language with generics.
https://en.wikipedia.org/wiki/Adjoint_functors