nLab
bounded chain complex

Definition

A chain complex $A_{•}$ is called

• bounded above if there exists $n\in \mathbb{N}$ such that $A_k=0$ for all $k>n$;

• bounded below if there exists $n\in \mathbb{N}$ such that $A_k=0$ for all $k<n$;

• 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