This is brand new to me, so forgive me if this is simple.
I understand the structure of a short exact sequence (the image of the current homomorphism is the kernel of the next), and I can understand why $\phi$ is injective in the below example. What's confusing me is that everywhere says that $\psi$ is surjective, but I cannot see why. I've consulted some textbooks but can't find any material on it, and any online explanations don't help either.
$${0}\rightarrow N\xrightarrow{\phi} G\xrightarrow{\psi} Q\rightarrow 0$$
Thanks in advance.
By the definition the image of $\psi$ is the kernel of the next homomorphism, which is the zero morphism $Q\to 0$. And the kernel of the zero morphism is entire $Q$. And so $im(\psi)=ker(Q\to 0)=Q$ or in english: $\psi$ is surjective.