I do know that maps/folds/etc. can be generalized to anything belonging to the functor class in #haskell; so things like trees and other "container" type things beyond just lists. However, I didn't want to introduce special terminology in what was otherwise free of such jargon.
As for the rest of what you said, I don't know enough category theory to understand what you meant, although I can recognize them as being category theory terms.
Thanks for pointing out the connections. Hopefully, one day I'll get to a level of understanding where I can grok what you said.