The nnn-th simplicial homology group of a Δ\DeltaΔ-complex XXX is the Z\mathbb{Z}Z-module HnΔ(X):=Hn(C∙Δ(X))H^\Delta_n(X) := H_n(C^\Delta_\bullet(X))HnΔ(X):=Hn(C∙Δ(X))