Cartesian monoidal category

Definition 15.3.3. A symmetric monoidal \(\infty \)-category \((D,\otimes )\) is called cartesian monoidal if the opposite symmetric monoidal \(\infty \)-category \((D,\otimes )\catop \) is cocartesian monoidal. We denote by \[ \Cat _{\infty }^{\otimes ,\cart }\subseteq \Cat _{\infty }^{\otimes } \] the full subcategory spanned by the cartesian monoidal \(\infty \)-categories.