# 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 $n \in \mathbb{N}$ such that $A_k = 0$ for all $k \gt n$;

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

• 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)