Fully faithful operad map

Definition 14.1.7. A morphism of \(\infty \)-operads \(f\colon \Oo \to \Pp \) is called fully faithful if for every finite set \(I\) and every collection of colors \(\{x_i\}_{i \in I}\) and \(y\) of \(\Oo \), the induced map \[ \Oo (\{x_i\}_{i \in I}; y) \to \Pp (\{f(x_i)\}_{i \in I}; f(y)) \] is an equivalence of animae.