Example 2.5.5.3. Let $X$ be a topological space. Then the singular chain complex $\mathrm{C}_{\ast }(X; \operatorname{\mathbf{Z}})$ is the chain complex of the singular simplicial set $\operatorname{Sing}_{\bullet }(X)$. In particular, the homology groups of the simplicial set $\operatorname{Sing}_{\bullet }(X)$ are the usual singular homology groups of the topological space $X$.
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