
morphism
If I have a mapping under addition $\displaystyle \alpha : \mathbb{z} \rightarrow \mathbb{z}$ given by $\displaystyle \alpha(h(x))=h'(x)$
to show it would I do this
$\displaystyle \alpha(h(x)+k(x))=\alpha h(x) + \alpha k(x)$
Then when mapping is applied $\displaystyle h'(x)+k'(x)=h'(x)+k'(x)$ and this shows that$\displaystyle \alpha : \mathbb{z} \rightarrow \mathbb{z} \alpha(h(x))=h'(x)$ is a homomorphism? or is there more?

Re: morphism
Hello
Your proof is correct. I suppose that your are considering $\displaystyle F$ only with que strucuture of group given by the usual adittion of funcitons.
Best regards.