constrained-categories

Haskell has, and makes great use of, powerful facilities from category theory – basically various variants of functors.

However, all those are just endofunctors in Hask, the category of all Haskell types with functions as morphisms. Which is sufficient for container / control structures that you want to be able to handle any type of data, but otherwise it's a bit limiting, seeing as there are (in maths, science etc.) many categories that cannot properly be represented this way. Commonly used libraries such as http://hackage.haskell.org/package/vector-space thus make little notion of the fact that the objects they deal with actually form a category, instead defining just specialised versions of the operations.

This library generalises functors etc. to a much wider class of categories, by allowing for constraints on objects (so these can have extra properties required). At the same time, we try to keep as close as possible to the well-known Haskell type class hierarchies rather than exactly adopting the mathematicians' notions.

Consider the README file, the examples, and/or the documentation to Control.Category.Constrained for how to make use of this.