Remark 6.2.4. If \(A\) is an abelian group regarded as a complex concentrated in degree \(0\), then Proposition 6.2.3 shows that \(HA\) is connective and that \(\Omega ^{\infty }HA\) is the discrete commutative group \(A\). Under the recognition equivalence of Theorem 5.4.6, it therefore corresponds to \(A\in \CGrp (\Set )\), giving a natural isomorphism \[ HA \iso \bB ^{\infty }A. \] Thus this construction agrees with the Eilenberg–MacLane spectrum of Definition 5.4.9.
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