Corollary 16.6.3. The tensor product functor \(- \otimes -\colon \Sp \times \Sp \to \Sp \) defined by Theorem 16.6.1 agrees with the one characterized by Proposition 4.4.16.
Proof. By parts (1) and (2) of Theorem 16.6.1, the tensor product preserves colimits in both variables, and the relation \(\S \otimes \S \simeq \S \) holds since \(\S \) is the monoidal unit. These are precisely the properties that determine the tensor product uniquely in Proposition 4.4.16, so the two agree. □
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