In Zieschang's "Theory of Association Schemes", in section 5.2, he remarks that the composition of homomorphisms is not always a homomorphism. I've been struggling to find an example of that claim. I've found certain papers which reference that fact, but I'm unable to find any example.
What would be a simple counterexample? By the lemma 5.2.1, the first homomorphism has to be non-surjective, so I've tried to find some simple examples for 2 or 3 element sets, but couldn't get it.
