You need to define the instance with `ChainableFunction' and not `CF' (the latter is value-level, not type level). Once you make that switch, you'll find yourself with an instance that is not compatible with the definition of the `Category' class. Prelude Control.Category> :info Category class Category cat where id :: forall a. cat a a (.) :: forall b c a. cat b c -> cat a b -> cat a c -- Defined in Control.Category We see that `id' and `.' have no class constraints and that there is in fact no where to place a class constraint on `a', `b' or `c'. I think that what you're looking for are "restricted categories" (and restricted monads and functors, as well, perhaps). A cursory search suggests the `data-category' package. -- Jason Dusek