[Haskell-beginners] Category question

[Manfred Lotz]

Hi there,
I know that this might be the wrong forum to ask. In this case I would
appreciate any hint where there is a good place to ask.

In the definition of a (mathematical) category it is said (among other
things), that for any object A there exists an identity morphism: 

idA: A -> A and if f: A -> B for two objects A, B then 

   idB . f = f and f . idA = f

must hold.

My question: Because I cannot think of any counterexample for the
last statement I would like to know if I just could omit this
from the definition and formulate this as a small theorem.

Or does there exist a counterexample where all conditions of a category
hold but there exist two objects A, and B where we have idB . f <> f
and/or f .idA <> f?



-- 
Manfred