Short exact sequence

Summary

A short exact sequence is an exact sequence $0 \to A \to B \to C \to 0$ whose first and last terms are zero. It says that $A$ is a subobject of $B$ and that $C$ is the corresponding quotient $B/A$. Short exact sequences are the basic input of homological algebra: functors are tested on them, and each gives a long exact sequence of derived functors.