Cocartesian symmetric monoidal category

Definition 15.2.20. Let \(\Cat _{\infty }^{\otimes ,\cocart } \subseteq \Cat _{\infty }^{\otimes }\) denote the full subcategory spanned by the symmetric monoidal \(\infty \)-categories of the form \((C,\amalg )\) for some \(\infty \)-category \(C\). We say that a symmetric monoidal \(\infty \)-category \((D,\otimes )\) is cocartesian monoidal if it is equivalent to \((C,\amalg )\) for some \(\infty \)-category \(C\) with finite coproducts.