ekmett
Reference for name "distributive"
Do you have a reference for the origin of the name "distributive"? The most relevant thing seems to be Linearly Distributive Functors but I can't see the connection.
Vocabulary wise, distributive comes just from the notion of a distributive law for a functor. This isn't, fundamentally, a directed notion. If you want a term with a better pedigree "Corepresentable" (or "Representable" if you don't want to be anal retentive about distinguishing covariance from contravariance with Co) functor.
To date, this has been split off from Data.Functor.Rep in adjunctions, because the latter required more than just Haskell 98. To be honest that isn't much of a going concern, and a slight improvement in the notion of distribution is enough to allow better performance and canonical implementation of the concept of a representation, so eventually I'd like to ship distributive v1 which changes the internal representation of the class considerably. This will entail shipping new versions of just about everything though.
The 1 branch is the current work-in-progress in that direction.
