Definition 5.3.4 (Commutative monoid). Let \(C\) be an \(\infty \)-category with finite products. We define a commutative monoid in \(C\) to be a product-preserving functor \[ M\colon \Span (\Fin ) \to C. \] We denote by \[ \CMon (C) \subseteq \Fun (\Span (\Fin ),C) \] the full subcategory spanned by the commutative monoids. We refer to the evaluation \(M(*)\) at the one-point set as the underlying object of \(M\). We will sometimes abuse notation and simply refer to \(M(*)\) as \(M\).
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