and
nonabelian homological algebra
A chain complex $A_\bullet$ is called
bounded above if there exists $n \in \mathbb{Z}$ such that $A_k = 0$ for all $k \gt n$;
bounded below if there exists $n \in \mathbb{Z}$ such that $A_k = 0$ for all $k \lt n$;
bounded if it is both bounded above and bounded below.