Notation 5.3.22. Let \(\Cat ^{\mathrm {prod}}_{\infty }\) be the subcategory of \(\Cat _{\infty }\) spanned by those \(\infty \)-categories that have finite products and the finite-product-preserving functors. We further denote by \[ \Cat ^{\sadd }_{\infty } \subseteq \Cat ^{\mathrm {prod}}_{\infty } \qquadtext { and } \Cat ^{\add }_{\infty } \subseteq \Cat ^{\mathrm {prod}}_{\infty } \] the full subcategories spanned by the semiadditive and additive \(\infty \)-categories, respectively.
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