nLab bounded chain complex

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

Contents

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

Revised on January 15, 2015 07:13:06 by Tim Porter (2.31.52.215)