Corollary 2.4.15. The functor \(\Pi _{\infty }(-)\colon \Top _* \to \An _*\) sends the topological \(n\)-sphere \(S^n \subseteq \R ^{n+1}\) to the homotopical \(n\)-sphere \(S^n\).
Proof. Since \(\Pi _{\infty }\) preserves coproducts, we have \(\Pi _{\infty }(S^0) \simeq S^0\). The claim now follows inductively from part (2) of Proposition 2.4.12. □
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