[Haskell-beginners] Category question

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