nLab bounded chain complex

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

Contents

Definition

A chain complex ${A}_{•}$ is called

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

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

• bounded if it is both bounded above and bounded below.

Examples

Revised on November 30, 2012 15:21:02 by Urs Schreiber (89.204.135.73)