Corollary 15.3.13. Let \(C\) be an \(\infty \)-category with finite products. Then associative algebras in the cartesian monoidal structure agree with associative operadic monoids in \(C\): \[ \Alg (C,\times ) \iso \Mon _{\Assoc }(C). \] Similarly, commutative algebras agree with commutative monoids: \[ \CAlg (C,\times ) \iso \Mon _{\Comm }(C)=\CMon (C). \]
Proof. This is the special case of Theorem 15.3.11 where \(\Oo =\Assoc \) and \(\Oo =\Comm \), respectively. □
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