Bounded chain complex of groups

Definition

Consider a chain complex of groups $(G_{n},d_{n})_{n\in \mathbb {Z} }$. We say that this chain complex is bounded if there exist integers $n_{1},n_{2}\in \mathbb {Z}$ such that:

• $G_{n}$ is the trivial group for all $n\geq n_{1}$.
• $G_{n}$ is the trivial group for all $n\leq n_{2}$.