  A careful account is given of generalized equivariant homology theories on
the category of topological pairs acted on by a group. In particular, upon
restriction to the category of equivariant simplicial complexes, the
equivalence of equivariant simplicial homology (also known as Bredon homology),
the second derived term of the Atiyah--Hirzebruch spectral sequence, and
equivariant singular homology is demonstrated.
