Lemma 4.4.29. For every \(k \in \Z \), the functor \(\pi _k\colon \Sp \to \Ab \) preserves arbitrary coproducts.
Proof. By Lemma 4.3.21, a filtered colimit of spectra is computed levelwise. The claim then follows from Exercise 4.4.23 together with the fact that the homotopy groups of pointed animae preserve filtered colimits. □
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