https://muratkasimov.art/Ya/Articles/Functors-represented-by-objects/
I’ve been working recently on functors that can be represented by objects - it was the missing piece of the puzzle that makes Я powerful enough to not use a class of custom functions! You can use this concept to initialise data structures, evaluate functions/stateful computations, do some scope manipulation. Other cases yet to be explored, but I’m pretty happy with the intermediate results.
The closest concept is Representable functors from this package except that (as in case with monads) you can use individual natural transformations.