[Haskell-cafe] The meaning of categories constructed from HASK

[Dimitri DeFigueiredo]

In category theory, there are many ways one can make new categories out
of an old one.

In particular, given a category C one can construct:

1. The arrows category of C:
        arrows in C become objects and
        commutative squares in C become arrows
2. The slice category of C given an object A:
        arrows into a distinguished object A become objects in the slice
        commutative triangles become arrows

There are also functors going from C to these new categories (and back).

Are these constructed categories useful when C = `Hask` (the category of
haskell types and functions)?
What do they represent in programming terms?

In other words, is there intuition for what the arrows category of Hask is?
What about the slice category of Hask over a specific type?
Do the functors between these match some programming abstractions?

Any pointers are much appreciated.

Thanks,

Dimitri