Proposition 8.2.6. The functor \(\pi _0\colon \Sp _{\geq 0} \to \Ab \) is symmetric monoidal, where \(\Ab \) is equipped with the usual tensor product \(- \otimes ^{\heartsuit } -\).
Proof. Under the symmetric monoidal equivalence \(\Sp _{\geq 0}\simeq \CGrp (\An )\) established in Part II (Corollary 16.6.5), this functor corresponds to the symmetric monoidal functor \(\pi _0\colon \CGrp (\An )\to \CGrp (\Set )=\Ab \) of Proposition 16.4.5. □
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