nLab
bounded chain complex

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

Definition

A chain complex A A_\bullet is called

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

  • bounded below if there exists nn \in \mathbb{N} such that A k=0A_k = 0 for all k<nk \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)