# nLab ordinary homology

### Context

#### Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

# Contents

## Idea

Ordinary homology is generalized homology with respect to an Eilenberg-MacLane spectrum $HA$, and often understood over $Hℤ$.

Equivalently this is computed by singular homology with coefficients in $A$.

## Properties

### Relation to homotopy groups

Ordinary homology with coefficients in $ℤ$ of a topological space $X$ serves to approximate the homotopy groups of $X$.

See for instance at

Created on August 31, 2012 16:57:24 by Urs Schreiber (89.204.139.6)