Remark 2.5.6.4. Let $M_{\ast }$ be a chain complex. We will generally not distinguish in notation between the simplicial abelian group $\mathrm{K}( M_{\ast } )$ and its underlying simplicial set. Note that $\mathrm{K}( M_{\ast } )$ is automatically a Kan complex (Proposition 1.1.9.9), which motivates our usage of the term “space”.

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