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.