Definition 7.6.6.1. Let $\kappa $ be an infinite cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We say that $\operatorname{\mathcal{C}}$ is $\kappa $-complete if admits $K$-indexed limits, for every $\kappa $-small simplicial set $K$.
We say that a functor of $\infty $-categories $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ preserves $\kappa $-small limits if it preserves $K$-indexed limits, for every $\kappa $-small simplicial set $K$ (Definition 7.1.4.4).