Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Construction 2.5.6.7 (Eilenberg-MacLane Spaces). Let $A$ be an abelian group, let $n$ be an integer, and let $A[n]$ denote the chain complex consisting of the single abelian group $A$, concentrated in degree $n$ (Example 2.5.1.2). We will denote the simplicial abelian group $\mathrm{K}( A[n] )$ by $\mathrm{K}(A,n)$ and refer to it as the $n$th Eilenberg-MacLane space of $A$.