Haskell is a purely functional language. However side-effects are (almost by definition) difficult to incorporate into a functional language. This is an important problem since I/O is a very important side-effect for most computer programs. Haskell's method of incorporating side-effects is to use monads.

One of the simplest ways to get a monad is from a pair of adjoint functors.

For more on monads see:  (1) embuchestissues.wordpress.com/2009/02/25/monads-in-mathematics-1-examples/

(2) A series of lectures on youtube by TheCatsters: http://www.youtube.com/watch?v=9fohXBj2UEI

Pairs of adjoint functors are fairly common and I've found they provide a useful way for seeing part of the "big-picture" in many different branches of mathematics.

Here's one of several introductions to pairs of adjoint functors:

concretenonsense.wordpress.com/2009/10/02/a-free-association-on-basic-adjoints/#more-713

Haskell is a purely functional language. However side-effects are (almost by definition) difficult to incorporate into a functional language. This is an important problem since I/O is a very important side-effect for most computer programs. Haskell's method of incorporating side-effects is to use monads.

One of the simplest ways to get a monad is from a pair of adjoint functors.

For more on monads see: 

(1) Embûches tissues blog: Monads in Mathematics 1: examples

(2) A series of lectures on youtube by TheCatsters:

Pairs of adjoint functors are fairly common and I've found they provide a useful way for seeing part of the "big-picture" in many different branches of mathematics.

Here is one of several introductions to pairs of adjoint functors from the Concrete Nonsense blog.