Catamorphisms for arrows?

Could Data.Foldable be extended to function types by way of Bananas in
Space: Extending Fold and Unfold to Exponential Types [1][2] or Boxes
Go Bananas: Encoding Higher-Order Abstract Syntax with Parametric
Polymorphism [3][4]?

1. http://citeseer.ist.psu.edu/293490.html
2. http://www.cs.nott.ac.uk/~gmh//bananas.ps
3. http://repository.upenn.edu/cis_reports/43/
4. http://www.seas.upenn.edu/%7Esweirich/abstracts.html#washburn+:bgb-journal

Jim