Notation 6.182.
Let \(K\) and \(K'\) be two classes of small categories. We write \(K \perp K'\), and say that \(K\) is complementary to \(K'\), if for every category \(C\) with \(K'\)-indexed colimits, the categories \(\Pp^K(C)\) and \(\Pp^{\all}_{K'}(C)\) define the same full subcategory of \(\PSh(C)\) (or of the category of small presheaves, if \(C\) is large), under the identifications from Remark 6.180.
Equivalently, the unique \(K\)-colimit-preserving extension
\[\Pp^K(C) \to \Pp^{\all}_{K'}(C)\]
of \(C \to \Pp^{\all}_{K'}(C)\) is an equivalence.