nLab
ordinary homology

Idea

Ordinary homology is generalized homology with respect to an Eilenberg-MacLane spectrum $HA$, and often understood over $H\mathbb{Z}$.

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

Properties

Relation to homotopy groups

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

See for instance at

• Hurewicz theorem

Related concepts

• ordinary cohomology