Warning 9.2.3.3. Let $\kappa $ be a regular cardinal. There is a slight tension between the terminological conventions of Definitions 7.6.6.6 and Definition 9.2.3.1:
According to Definition 7.6.6.6, an $\infty $-category $\operatorname{\mathcal{C}}$ is $\kappa $-cocomplete if it admits $K$-indexed colimits for every $\kappa $-small simplicial set $K$.
According to Definition 9.2.3.1, an $\infty $-category $\operatorname{\mathcal{C}}$ is $\kappa $-sequentially cocomplete if it admits colimits indexed by the $\infty $-category $\operatorname{N}_{\bullet }( \mathrm{Ord}_{< \kappa } )$.
Neither of these conditions implies the other (the linearly ordered set $\mathrm{Ord}_{< \kappa }$ has cardinality $\kappa $, and is therefore not $\kappa $-small). Instead, they should be viewed as complementary to one another: see Corollary 9.2.3.9.