In the proof that "in the category Div of divisible (abelian) groups and group homomorphisms between them there are monomorphisms that are not injective" given in Wikipedia http://en.wikipedia.org/wiki/Monomorphism (see the Examples section) , the proof assumes at one point that $h(y) \in \mathbb Z$ , I don't understand this , please help
EDIT : one other thing ; at the end , they take the morphisms $f,g$ with range deliberately $\mathbb Q$ and not arbitrary divisible groups , why is that ?
The map $h: G \rightarrow \mathbb{Q}$ in the example is a function with the property $q \circ h = 0$ where $q : \mathbb{Q} \rightarrow \mathbb{Q}/\mathbb{Z}$ is the quotient map. Now note that the property $q \circ h = 0$ is equivalent to $h(x) \in \mathbb{Z}$ for all $x \in G$, in particular we have $h(y) \in \mathbb{Z}$.