nLab bounded chain complex

Definition

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.

Examples

• A connective chain complex is bounded from below.

Related concepts

• category of chain complexes

  • chain complex, connective chain complex

  • chain map, quasi-isomorphism

  • chain homotopy

  • model structure on chain complexes

  • elliptic chain complex

• cochain complex

• filtered chain complex

• perfect chain complex