nLab bounded chain complex

Contents

Context

Homological algebra

homological algebra

(also nonabelian homological algebra)

Introduction

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Schanuel's lemma

Homology theories

Theorems

Contents

Definition

A chain complex A A_\bullet is called

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

  • bounded below if there exists nn \in \mathbb{Z} such that A k=0A_k = 0 for all k<nk \lt n;

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

Examples

Last revised on January 15, 2015 at 07:13:06. See the history of this page for a list of all contributions to it.