Short exact sequence
= Short exact sequence
{wiki=Exact_sequence}
A short exact sequence is an exact sequence
$$
0\longrightarrow L\xrightarrow{j}M\xrightarrow{q}N\longrightarrow0.
$$
Thus $j$ is injective, $q$ is surjective, and $\operatorname{im}j=\ker q$.