I have the category of pointed rings. Objects are all pairs $(R, r)$ where $R$ - ring (with 1) and r is the element of R. Morphisms are homomorphism of rings. Morphism $(R, r) \longrightarrow (R', r')$ exist if exist homomorphism p: $R \longrightarrow R'$ and $p(r)=r'$.
Can somebody help to find initial object or proof that it doesn't exist? I think that it doesn't exist but can't find a way to proof.