The categorical dual of Traversable (Data.Distributive in Haskell). This is a structure that builds on Functor and is an expression of distributive laws (an arithmetic example is a(b + c) = ab + ac).
Due to the lack of non-trivial comonoids in Haskell, we can restrict ourselves to requiring a Functor rather than some Coapplicative class. Categorically every Distributive functor is actually a right adjoint, and so it must be Representable endofunctor and preserve all limits. This is a fancy way of saying it isomorphic to (->) x for some x.
To be distributable a container will need to have a way to consistently zip a potentially infinite number of copies of itself. This effectively means that the holes in all values of that type, must have the same cardinality, fixed sized vectors, infinite streams, functions, etc. and no extra information to try to merge together.
See Data.Traversable by Edward Kmett.
